Tagged Questions

This tag is for questions where the poster seeks references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.

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1
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1answer
58 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
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7answers
120 views

Text books on computability

I collected the following "top eight" text books on computability (in alphabetical order): Boolos et al., Computability and Logic Cooper, Computability Theory Davis, Computability and unsolvability ...
1
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0answers
28 views

EGA reference for equivalent criteria for ampleness

Let $X$ be a projective scheme over a field $k$ with $\mathcal{L}$ a very ample line bundle on $X$ (very ample here means relative to the structure morphism $X \to \operatorname{Spec} k$. Where is it ...
1
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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 ...
1
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0answers
21 views

Computations of common isometry groups, $O(n)/O(n-1), SO(n)/SO(n-1), U(n)/U(n-1)$, etc?

On wikipedia, some of the common isometry groups are given: $S^{n-1}\cong O(n)/O(n-1)$, $S^{n-1}\cong SO(n)/SO(n-1)$, etc. Is there a reference where some/any of these groups are computed? I'm just ...
10
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2answers
235 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 ...
1
vote
1answer
31 views

Is there a Poincare lemma for codifferential?

Is every co-closed form also locally co-exact? That is for each $k$-form $\omega$ such that $\delta \omega = 0$ there exists $(k-1)$-form $\eta$ for which locally $\omega = \delta \eta$. My current ...
1
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0answers
32 views

Ordinary differential equations book recommendation

I am looking for a book about the theory of ordinary differential equations. I dont need much computation driven textbook, one for the engineers or science students, but mostly the theory based one. ...
6
votes
2answers
92 views

Any Good Textbook on ODE that covers the following topics…

I am a first year graduate student in math. I am taking a graduate course on ODE which covers the topics listed below. I feel that the lecture notes of my instructor are great. However, like with any ...
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
2
votes
0answers
48 views

Large Cardinal Consequences of $\kappa$-Suslin Hypothesis

$\kappa$-Suslin Hypothesis ($\kappa$-SH) for the infinite regular cardinal $\kappa$ says that every tree of height $\kappa$ either has a branch of length $\kappa$ or an antichain of cardinality ...
3
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1answer
122 views

Books with collections of unusual and advanced integration techniques

I am searching for some comprehensive books that collect, explain, and provide examples of extremely advanced and/or unusual integration techniques. Can you point out some good references? Note: ...
2
votes
0answers
91 views

The history of summations

How did summations evolve? For instance, is there an article, book, webpage, etc. that talks about how mathematicians came up with using $\sum_x{ f(x) }$? I'm very interested on how summations came ...
0
votes
0answers
7 views

What is the relation between the upper bound,low bound of simple continued fraction expansion of quadratic algebraic numbers and the integer

What is the relation between the upper bound,low bound of simple continued fraction expansion of quadratic algebraic numbers and the integer As we know,$\sqrt{14}= [3;1,2,1,6,1,2,1,6…]$,let $B_u,B_l$ ...
0
votes
1answer
59 views

Difference between type and similarity type

In usual terminology, is there a difference between the type and similarity type? Is there a general consensus for the definition of the two terms? Please suggest to me books where I can study these ...
0
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0answers
17 views

Formalization of mathematical expressions

Is there some literature out there that defines mathematical expressions rigorously? For example, we want to say that "(2+2)" and "(1+3)" are different expressions, and both are different from ...
2
votes
0answers
49 views

Derivative and Integrals of Matrix functions

I am interested in calculating quantities such as $$\frac{\operatorname{d}}{\operatorname{d}\!t} e^{A(t)},\quad \frac{\operatorname{d}}{\operatorname{d}\!t} e^{\int_{a}^{t}A(s)\operatorname{d}\! s}$$ ...
2
votes
1answer
53 views

Electromagnetism and thermodynamics(Statistical mechanics) books for the mathematician?

I found some very good classical and quantum mechanics,special relativity,gauge theory books for the mathematicians,but I couldn't find anything on electromagnetism or thermodynamics,are they of not ...
1
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0answers
23 views

Practical determinations of trigonometric identities

I am looking for articles, or any reference, that detail practical determinations of trigonometric identities, with particular emphasis on trigonometric functions raised to the power of 3 or higher. ...
1
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0answers
34 views

A program for draw differential equations

I need to analyze the autonomous equation $ \ddot x +x +\alpha x^2 = 0 $ I need to analyze its flow about its critical points, can you suggest me a program in which I can draw this equation ( $\dot x ...
3
votes
1answer
61 views

Special reference for differential geometry

I am not entirely sure how to formulate the question, but here it is. I am looking to start a self study on general relativity, and of course I need a good grasp on semi-riemannian geometry (I am ...
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 ...
1
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0answers
82 views

Has anyone seen this form of the Collatz Conjecture?

This question asks if this form of the Collatz Conjecture has been reported or is all ready known. The goal of this question is to determine if I should write a paper on it's discovery or not and ...
-1
votes
1answer
53 views

Original Mathematical biology book? [closed]

Are there any book that join math with biology in a way that's different from all those books you can easily find on amazon ?
2
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0answers
31 views

Methods to prove axiom independence

What methods have been used to prove the independence of axioms? For instance, in many abstract algebra books the axiom of choice is stated to be independent of all the other axioms of set theory, but ...
4
votes
0answers
55 views

Newton's Investigation of Cubics: Generalization?

I recently read about Newton's investigation of cubic curves, and how, like for quadratic curves we can classify them into parabolas, ellipses and hyperbolas, Newton was able to classify cubic curves ...
7
votes
1answer
113 views

Is there a codifferential for a covariant exterior derivative?

For forms on a Riemannian $n$-manifold $(M,g)$ there is a notion of a codifferential $\delta$, which is adjoint to the exterior derivative: $$\int \langle d \alpha, \beta \rangle \operatorname{vol} = ...
5
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2answers
208 views

Second year mathematics textbook recommendations.

I am currently majoring in pure mathematics, and would like to purchase textbooks that would not only assist with content covered in the courses, but will serve as a great reference throughout my ...
0
votes
0answers
20 views

Books for Random Process

I have been using Sheldon Ross' book all through undergrad and recently I've noticed that it does not cover random process at all. What are some good references on this material that does not treat ...
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 ...
1
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0answers
104 views

What happens if we rotate the kernel of an integral operator?

Given an integral operator $K$ on $L^2(\mathbb R)$ with kernel $k(x, y)$, consider the integral operator $L$ on $L^2(\mathbb R)$, whose kernel has the form $k(\alpha x+\beta y, \gamma x+\delta y)$, ...
2
votes
2answers
102 views

Set theory and physics [closed]

I would like to know if there are some physical concepts (preferably accessible ones like force, torque, ...) that can be significantly better understood when looked at in the light of concepts taken ...
4
votes
1answer
64 views

Are there any large cardinal properties of the critical point of a $j: L \longrightarrow L$?

I've recently been thinking a bit about $L$ and $0 \sharp$. As is well known, the existence of $0 \sharp$ is equivalent to the existence of a non-trivial elementary embedding $j: L \longrightarrow ...
0
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0answers
21 views

I am looking for a good primer on Special relativity. [migrated]

I am starting a course in Gravity and Quantum Field Theory this year, and I have all of the prerequisites except for a few topics in Special Relativity. I have had some SR, but only the 1-dimensional ...
0
votes
0answers
41 views

book for Elliptic Partial Differential Equations

I want to have a very beginning introduction to holder,morrey,campanato space, hilbrt 19th problem, Regularity in Lp spaces, Schauder theory what books or notes do you suggest me to read? I just ...
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? ...
3
votes
0answers
72 views

Real Analysis texts: Royden versus Stein & Shakarchi. Which is better? (and other suggestions welcome)

I am taking an introductory "graduate" analysis class and am comparing Analysis books that cover measure theory. I have had an "advanced calculus" class that covered the standard topics. I am having ...
0
votes
2answers
37 views

The Chernoff bound for continous rendom variables.

In a paper I am reading, authors apply the Chernoff bound to a continuous random variable $X$ with positive mean: $$\mathbb{P}(X\le 0)\le \mathbb{E}[\exp(\lambda X)]$$ I do not understand it. When I ...
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 ...
0
votes
0answers
15 views

Deck transformations and Gromov Hyperbolicity

I would like to ask, once more, for some references in Gromov-hyperbolic spaces. The question is specifically the following: Does someone know any alternative reference, alternative proof, anything, ...
6
votes
0answers
120 views

Isaac Newton did number theory?!

I was reading Whiteside's article called "Newton the Mathemtician", where he says that Newton did Number Theory (e.g. inverstigating which numbers are expressible as a sum of two cubes). If this is ...
8
votes
8answers
435 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 ...
2
votes
1answer
47 views

Computation of adjoint functors (sheafification)

In a (complete) category, limits can be "computed" assuming one knows how to compute products and equalisers. I have seen it mentioned that adjoint functors can be found using certain ...
0
votes
2answers
34 views

References for Linear Algebra needed for Differential Equations and Linear Programming

I am in need of learning the Linear Algebraic theory behind the following Applied disciplines. Could someone please recommend Linear Algebra books for: Differential Equations: Specifically learning ...
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 ...
3
votes
1answer
75 views

Reference Request to Prepare for Hatcher's “Algebraic Topology”

Hatcher himself has an excellent and always generously free set of notes on point- set topology: http://www.math.cornell.edu/~hatcher/Top/TopNotes.pdf It includes up to quotient spaces. It seems ...
7
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3answers
159 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 ...
0
votes
1answer
25 views

Introduction to Reidemeister--Schreier Method

I am learning Reidemeister--Schreier method, a method determining explicitly presentations for subgroups of a given group. Can anyone recommend some introductory material, preferably those with ...