1
vote
1answer
25 views

What is Neyman-Pearson lemma? Why is this proof of Neyman-Pearson's lemma look so diffcult?

What is Neyman-Pearson lemma? Why is this proof of Neyman-Pearson's lemma look so diffcult? I am consider taking a undergraduate course in my college called mathematics of statistics and in the ...
1
vote
1answer
67 views

who, by doing what, can make major contributions (breakthrough/discoveries) in math research?

I am a Math Ph.D student, had already published two small articles. I want to ask more experienced mathematician a question. What kind of person, by doing what, can make major contributions ...
3
votes
0answers
62 views

Except First year Abstract Algebra and commutative Algebra, what else do i need to start read Algebraic Geometry text?

Except First year Abstract Algebra and commutative Algebra text, what else do i need to read before start read Algebraic Geometry texts? I am refer to the beginning texts: "Algebraic geometry an ...
3
votes
1answer
48 views

What is a list of book that i need to read as a prerequisite before start reading “lectures of logic and set theory vol.1 by George Tourlakas”?

What is a list of formal textbook that i need to impose myself to read as a prerequisite before start reading a book called lectures of logic and set theory vol.1 by George Tourlakas? That book is ...
4
votes
4answers
125 views

Good books written by great mathematicians

I read many of Richard Fenynman's books and I found them both very entertaining and moving, showing the human side of a brilliant scientific mind. I recently read also a collection of P.A.M. Dirac's ...
3
votes
1answer
41 views

Self-learning Book recommendation for topics in ring-theory

I failed badly in my Internal examination in ring theory , and at any cost want to improve upon my grades in the final eamination,with a month and a half to go .... I haven't yet covered the below ...
0
votes
0answers
19 views

Any book on timeline of progress of Math concepts and applications

I was wondering if there is any book that chronicles the progress of Math over the centuries and also mentions about how/when applications of various theories were discovered/invented. I have been ...
2
votes
0answers
65 views

Second reading on set theory?Any recommendations?

I have in past six-ish months studied through the Herbert Endertons Elements of set theory book. Up to the point the book is great,I loved most parts of it and learned almost everything up to the ...
1
vote
1answer
33 views

Connections between SDE and PDE

I have encountered a number of situations where the solution of a PDE and a certain expectation associated to a Markov process are equal. Two examples include: The heat equation $u_t = \Delta u$ ...
6
votes
1answer
123 views
+50

Reference request regarding calculus exam

I'm currently a first year computer science student and I'm deeply interested in calculus . That being said, what we studied so far consists of: Cantor sets, sequences and a brief introduction to ...
0
votes
0answers
31 views

Maturity and Proficiency in calculus, linear algebra for successful research

Will the high level maturity and proficiency in basic calculus, linear algebra (both calculation and theorem aspects) be required or recommended as an important factor to be successful in mathematical ...
4
votes
2answers
129 views

Are all calculus textbooks “the same”?

I'm not satisfied with my calculus textbook,[1] and because of that I have searched for books by other authors. The problem is: all the books I have taken a look at are almost the same, even the ...
2
votes
1answer
32 views

Other Useful Series Tests

So after taking calculus II, or maybe a first course in analysis, everyone learns a few series tests. They learn 1) Divergence Tests 2) Integral Test (from which we deduce things like $p$-series. ...
0
votes
0answers
33 views

A linear algebra textbook that is advanced enough as a prerequisite to read time series and econometric textbook?

A linear algebra textbook that is advanced and comprehensive enough as a prerequisite to read time series by Hamiliton and econometric by Hayashi? If possible, please also answer on which statistics ...
6
votes
0answers
96 views

Pre-requisites and references for $K3$ surfaces

I would like to know the "roadmap" to study $K3$ surfaces. Perhaps, my background might be helpful: I am an undergraduate student, who knows the basics of Differential Geometry, Topology, Complex ...
16
votes
4answers
231 views

Value in retracing mathematicians' steps (specifically Galois)?

So I'd like to learn Galois Theory, which I am probably not "qualified" for in an ordinary sense (I've never done abstract algebra, and I'm just now learning linear algebra in my vector calculus ...
12
votes
8answers
236 views

Mathematicians' manual of style

I know that there are many styles to write citations and footnotes and that they are all equally good (as long as the reference is complete), but I would like to know if mathematicians follow some ...
0
votes
0answers
57 views

Mathematics only with physics? What about biology and chemistry?

In The Mathematical Mechanic, the author "reveals how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways ...
1
vote
2answers
163 views

Friends and Enemies of Infinities [closed]

Infinity is a dividing line in the community of mathematicians. There is a long standing contest between those who believe in rich theory of infinite mathematics and large infinite numbers and those ...
1
vote
1answer
49 views

Differential-geometry textbook with solved problems

I'm looking for a textbook in differential geometry which inside has exercises with (at least) final answers. Since it's my first course in differential geometry it doesn't have to cover material (we ...
2
votes
0answers
41 views

Typical course of study chart [closed]

I am an undergraduate student in math and am very interested in the field. I have bought a few books and self-studied on my own as i have free time. The next book i found on amazon was riemannian ...
2
votes
0answers
86 views

Algebraic approach to analysis

Can topics and foundations of real analysis be interpreted and profitably explained in terms of abstract algebraic structures? If so, what papers or books (accessible to undergraduate students) ...
2
votes
3answers
173 views

Big list of books on counterexamples and other clever observations in different topics

This question is related to Counterexample Math Books, but I'm looking for books in areas which aren't covered there (for example, number theory). In addition, books that focus on clever ...
2
votes
0answers
98 views

Learning Roadmap to Mathematical Physics

Currently, I am a graduate student specializing in algebraic geometry. On the other hand, I have also become extremely interested in the mathematical physics. However, I am not sure what steps I ...
1
vote
0answers
58 views

Big list of fun mathematical book to “play” with classmates

I am searching for some fun maths books "have fun" (mathematically) with my classmates. To give you a better idea of what I'm looking for, I'll mention some books that I find suitable: Roger B. ...
-2
votes
2answers
95 views

Best Mathematical Logic Books the Style of Which is Like a Mathematics Publication rather than a Logic Publication?

I found many good mathematical logic books are written like a publication in the field of Logic. For instance, in such books I would see such as "For every $x$, if $x$ is a real number then $x^{2} ...
5
votes
1answer
103 views

Guide to mathematical physics?

I am currently a math phd student specializing in algebraic geometry aspiring to work at the boundaries of the the fields of mathematics and physics and so, was looking into the field of mathematical ...
1
vote
1answer
59 views

Useful techniques of experimental mathematics (reference request)

I am searching for papers or books that explain thoroughly useful interesting techniques of experimental mathematics that can be understood and profitably applied by an undergraduate student.
8
votes
1answer
130 views

Reference request: books that describe application of physical reasoning to mathematical problems

I am searching for more books like Uspenski's Some applications of mechanics to mathematics and Levi's The Mathematical Mechanic. In other words, I am looking for books that show interesting and ...
1
vote
0answers
44 views

Dilemma for Studying Probability Theory while Waiting to Learn Measure Theory

I'm taking stochastic probability class but I'm now only taking analysis (with Rudin's PMA) class. The stochastic probability class doesn't depend heavily on the theoretic structures: rather, the ...
10
votes
2answers
236 views

Abstract algebra book with real life applications

Is there an abstract algebra book that emphasizes the applications to "real world" problems? Update: By real world, I mean mostly related to physics or other sciences. But references to coding theory ...
8
votes
0answers
75 views

Mathematical dress fashion [closed]

I don't understand, was it a fashion in the 17th/18th centuries among mathematicians to wear a towel on your head and striped pyjamas? Brook Taylor Leonhard Euler
0
votes
2answers
100 views

Best practices in notation

I have already read A Primer of Mathematical Writing, by Steven Krantz which gives extremely good advice about writing mathematics. But I would like to collect some more specific suggestion about ...
2
votes
0answers
102 views

Game theoretical approach to other branches of mathematics

Are there some methods and ideas derived from game theory that are successfully applied to better (or more intuitively) understand theorems and proofs or tackling problems from other areas of ...
0
votes
1answer
19 views

book for study finite element method

I want to study finite element method for study partial differential equations in particular for parabolic type equation. Can you recommend a book which includes espesially mathematical background? ...
17
votes
5answers
354 views

Big list of serious but fun “unusual” books

I would like to have some suggestions about serious (that is, with good mathematical content) but fun books that cover topics (or propose problems) in "recreational mathematics"; in any other field ...
8
votes
8answers
436 views

Mathematical breakthroughs [closed]

When I read about mathematical history I hear of breakthroughs. For example, Cartesian geometry, Newton/Leibniz Calculus, and so on. My question is this: What are some recent epoch-making ...
3
votes
3answers
83 views

Elementary geometry from a higher perspective

I'm searching for some references that deal with topics from "elementary geometry" analysing them from a "higher" perspective (for example, abstract algebra, linear algebra, and so on).
3
votes
5answers
175 views

Suggestion: good book on probability theory with emphasis on applications to other areas of mathematics and physics

On this website, there are many questions about books on probability theory, but I would like to ask if you can suggest a book (or more than one if necessary) that is: rigorous and accurate ...
7
votes
3answers
160 views

Books that you think you should have read during your undergraduate years

A quite popular question here is "If you could go back in time and tell yourself to read a specific book at the beginning of your career as a mathematician, which book would it be?" I would like to ...
5
votes
0answers
65 views

Legitimate papers refuting the significance of the golden ratio in art?

I'm not sure this is the right place to ask about this, but is there any legitimate peer-reviewed paper refuting the significance of the golden ratio in art? I can find numerous websites and blogs ...
20
votes
7answers
2k views

Very *mathematical* general physics book

I am searching for a book to study physics. So far, I've been suggested Resnick, Halliday, Krane, Physics, but it doesn't seem to be very suited for a math major. Can you suggest some more ...
2
votes
1answer
80 views

Thinking and writing about mathematical structures in a way that is rigorous and precise.

Working inside a particular mathematical structure, I have no trouble giving rigorous definitions, nor deciding whether or not a definition is rigorous. For example, working inside $\mathbb{Z}$: ...
0
votes
0answers
60 views

Exercise books in abstract algebra and number theory

I'm studying Herstein's Topics in algebra and Hardy&Wright's An introduction to the theory of numbers, and I was wondering if there are some exercise books (that is, books with solved problems and ...
2
votes
4answers
149 views

Exercise books in linear algebra and geometry

I'm studying Brannan's Geometry and Lang's Introduction to Linear Algebra and I was wondering if there are some exercise books (that is, books with solved problems and exercises) that I can use as ...
6
votes
3answers
223 views

Exercise books in analysis

I'm studying Rudin's Principles of mathematical analysis and I was wondering if there are some exercise books (that is, books with solved problems and exercises) that I can use as a companion to ...
5
votes
4answers
214 views

Books that use probabilistic/combinatorial/graph theoretical/physical/geometrical methods to solve problems from other branches of mathematics

I am searching for some books that describe useful, interesting, not-so-common, (possibly) intuitive and non-standard methods (see note *) for approaching problems and interpreting theorems and ...
4
votes
1answer
120 views

Novel approaches to linear algebra and geometry

I'll be studying Brannan's Geometry and Lang's Introduction to Linear Algebra for one university course. I would like to know if you can you suggest some books that offer a unique perspective on the ...
11
votes
6answers
358 views

Book with novel approaches to analysis

Now I'm studying Rudin's Principles of mathematical analysis, but I'm searching for a book that offers geometric, physical or otherwise non-standard approaches to topics in analysis. Also, I'm looking ...
2
votes
1answer
60 views

Software for math sketching

Usually when you're writing in LaTeX you want some pretty illustrations. Right now for geometry figures I use GeoGebra, which is easy enough; but I usually see better figures on other papers. Plus, ...