Tagged Questions
22
votes
2answers
312 views
English words in written mathematics
I recently marked over $100$ assignments for a multivariable calculus course. One question which a lot of people did poorly was proving a given set was open. Aside from issues relating to rigour and ...
4
votes
3answers
99 views
How to fill gaps in my math knowledge?
Just finishing highschool, even though I am doing "well" (in the context of the math course itself), I have significant holes in my actual math knowledge.
As I think many people who explore math ...
6
votes
0answers
67 views
Accessible introduction to category theory from the point of view of preorders. [duplicate]
Are there books renowned for introducing category theory in a very accessible way? An emphasis on the point of view that categories generalize preorders would be especially appreciated.
My goal is to ...
0
votes
0answers
34 views
What do I need to know to understand Lagrange multipliers?
I've seen Lagrange multipliers used as a powerful method for tackling inequalities and some IMO problems, and I'm aware that it's a part of calculus. I'm currently taking BC Calculus in high school, ...
3
votes
1answer
102 views
Differential Geometry without General Topology
I want to ask if there is some book that treats Differential Geometry without assuming that the reader knows General Topology. Well, many would say: "oh, but what's the problem ? First learn General ...
2
votes
0answers
111 views
Is it possible to learn mathematics right from the source instead of reading textbooks. By studying the masters and not their pupils
i was wondering if mathematics learning process require the use of textbooks.
When i was a high school student, i read as a preparation for university, Legendre book on Elements of geometry and ...
2
votes
1answer
105 views
What is a good book to learn number theory?
What would be a good book to learn basic number theory? If possible a book which also has a collection of practice problems? Thanks.
0
votes
1answer
41 views
Topic for presentation on Group Representations, Young Tableaux, Symmetric Group
I need to do a presentation relating to group representations/Young tableaux/symmetric group; however, for all my searching, I cannot find a cool topic that I find personally interesting (and that is ...
3
votes
1answer
37 views
Foundation on Diophantine Analysis and Number Theory
I want to read particularly about diophantine Analysis and Number Theory from a novice level.
The books which I found on net:
A Guide to Elementary Number Theory by Underwood Dudley
Diophantine ...
2
votes
2answers
88 views
Which undergraduate math book cover topics about polynomials?
In China, there's a course called “Advanced Algebra," the first chapter of this course is all about polynomials, I wonder which undergraduate math books cover this topic?
The details are below, sorry ...
8
votes
1answer
132 views
Real analysis textbok that develops the subject in a self-motivated, coherent fashion?
Well, it seems as though I just failed my analysis prelim for the second time... I have one more try in about $5$ months.
I'm failing to build up a framework for how to think about analysis problems. ...
7
votes
4answers
213 views
A Math book with an inspiring ethos?
I was for some time curious about William Feller's probability tract (first volume); luckily, I could lay my hands on it recently and I find it of super qualities. Its provides a complete exposition ...
6
votes
1answer
214 views
Is there a rigorous theory of context, whereby sets can gain additional structure within a context?
Consider sets $G$ and $H$ and a function $f : G \rightarrow H$. So far, it doesn't really make sense to ask whether $G$ and $H$ are groups (technically, the answer is "no, they're not groups"), and ...
3
votes
0answers
65 views
$M_n=2^n-1$ Mersenne numbers in mathematics
Did the Mersenne numbers turn out to be interesting in other fields of mathematics besides the Numbers Theory?
In other words, the function $M(n)=M_n$
where
$$M_n=2^n-1$$
or the recursive realtion
...
7
votes
2answers
194 views
Connection between algebraic geometry and high school geometry.
if there is one thing that going to math competitions has taught me it is that I suck at high school olympiad level geometry. However I often find solace in the fact that not a lot of mathematicians ...
4
votes
1answer
41 views
Literature request - Classification of periodic holomorphic functions
For a seminar, I received the assignment to present the classification of periodic holomorphic/meromorphic functions. I have access to a limited amout of resources that I receive from my lecturer - ...
7
votes
1answer
89 views
The collection of pathological examples in one reference - Reference request
I would like to ask whether there is a reference which collects pathological examples in mathematics (in general). What I mean is that, for instance, consider Weierstrass function. It has the ...
2
votes
2answers
94 views
How is “1” defined in various branches of mathematics?
Wikipedia does not elaborate much on the concept of "One" in such branches as graph theory, ring theory, algebra, topology, measure theory, formal logic, etcetera. How can one grasp the concept of ...
6
votes
1answer
116 views
Is this an interesting generalization of the notion of an open set?
Let $X$ denote a topological space. Some subsets $A \subseteq X$ might have the property that $\partial A = \partial(\mathrm{int}\,A).$ This is certainly true if $A$ is open (since open implies ...
2
votes
3answers
148 views
Mathematical applications of ordinary differential equations.
I'm looking for more mathematically oriented applications of ODEs (if possible of first order equations). I've browsed through several books and they are all full of physics applications and very ...
6
votes
2answers
153 views
Filling the gap in knowledge of algebra
Recently, I realize that my inability to solve problems, sometimes, is because I have gaps in my knowldge of algebra. For example, I recently posted a question that asked why $\sqrt{(9x^2)}$ was not ...
23
votes
8answers
842 views
How to use math textbooks
I'm a higher schooler who was recently gifted a book by my teacher (Schaum's outline of advanced calculus) which is really awesome and I've started working my way through it.
I have run into a ...
2
votes
2answers
52 views
Why is $S/R$ a ring extension?
If $S$ is a ring and $R \subset S$ is a subring it's common to write that $S/R$ is an extension of rings. I frequently find myself writing this and read it quite often in textbooks and lecture notes. ...
17
votes
3answers
461 views
What's next for me?
I'm in my last year of undergrad, and I would like to do original research for my senior thesis. I am already published in finite group theory and am looking for a new topic to study.
I have taken ...
10
votes
2answers
249 views
Choosing an advanced group theory text: concerns
In this question, An Introduction to the Theory of Groups by Rotman is recommended twice as a good second-course group theory text. However, after reading the reviews here, and seeing this pdf of ...
1
vote
0answers
58 views
Applications of prime-number theorem in algebraic number theory?
Dirichlet arithmetic progression theorem, or more generally, Chabotarev density theorem, has applications to algebraic number theory, especially in class-field theory.
Since we might think of the ...
0
votes
3answers
146 views
Reference request - being rigorous about a common abuse of notation.
I've completely rewritten this question, in accordance with this advice.
As a motivating example, suppose we're working in ETCS. Let $\bar{1}$ denote the canonical singleton set, and assert that by ...
4
votes
2answers
56 views
Books for linear algebra over commutative rings
I was thinking about reviewing linear algebra to recover many theorems that I can use over commutative rings with unity. But it seems very tedious and I did not want to make any mistakes on these ...
0
votes
1answer
109 views
Functional Analysis - Where to go from here?
The short version of this question is this:
I like functional analysis and want to learn more. I've taken a class on it and I've read the books by Brezis and Conway. Where can I go from here? Do
...
1
vote
4answers
154 views
Best practice book for calculus
I tried with every inch in me to not ask a question such as this but I just couldn't resist asking this.
What is the best Calculus practice book?
I tried looking around but couldn't find a ...
3
votes
1answer
56 views
What are all isometry classes of the 2-sphere?
In topology, one learns how to classify the compact surfaces up to homeomorphism. And in fact, since "homeomorphic" and "diffeomorphic" coincide in dimension 2, we can classify the compact (smooth) ...
1
vote
2answers
90 views
Math resources for electrical engineering?
I am considering electrical engineering as my field of study.
However, my math knowledge might not be as good as it should be.
What math books/resources would you recommend me to read?
4
votes
2answers
210 views
Where to go after Advanced Calculus 2?
I will be finishing up Advanced Calculus 2 soon and I would like to continue self studying Analysis. I want to learn Real and Complex Analysis, Measure Theory and all that other good stuff. but I am ...
1
vote
0answers
103 views
Mathy things that do not exist in the real world [closed]
There are things like $x^2$ which mirror an area, which is something that exist in the real world. The same applies to $\pi$, to integers, and many other things.
Are there, on the other hand, things ...
3
votes
0answers
51 views
References about finite group theory
In your opinion which are the best books regarding the theory of finite groups? I think that a wonderful one is "Finite Group Theory - Michael Aschbacher".
Many thanks.
3
votes
1answer
121 views
Looking for comic about mathematics teacher
Apologies if this question is considered off-topic on this forum.
Somewhere in the 1990s, I saw a comic (newspaper comic, but I don't remember which newspaper) about a mathematics teacher. His school ...
0
votes
1answer
166 views
possible topics for undergraduate project. [closed]
i don't know whether it will be appropriate to ask this question here or not but i need help.
we have to a project in either pure or applied mathematics. my supervisor told me that it should not be ...
1
vote
1answer
44 views
Conference and workshops
Is there any website which keep track of the upcoming workshops and conferences in Mathematics and related areas. For me,manytimes come accross it after it's over. Is there any way to deal with this ...
2
votes
1answer
93 views
Hydra game and quantum superposition
Goodstein's theorem is not provable in Peano Arithmetic showed by Kirby and Harrington in 1982 [Wolfram Mathworld].
Any reference of a "quantum" hydra game where a head can remain in a state of ...
11
votes
3answers
247 views
Explaining what real math is to a high school student
I think, after reading through some of the questions here and their answers, that there are many people here who share my opinion on high school mathematics that it's quite different from "real ...
1
vote
3answers
238 views
What is more elementary than: Introduction to Stochastic Processes by Lawler
I have trouble to reading this book!
What book is more elementary/preliminary than this book: Introduction to Stochastic Processes by Lawler
10
votes
1answer
143 views
Counterexample Math Books
I have been able to find several counterexample books in some math areas. For example:
$\bullet$ Counterexamples in Analysis, Bernard R. Gelbaum, John M. H. Olmsted
$\bullet$ Counterexamples in ...
1
vote
1answer
107 views
Book recommendation request for geometric bodies (cube, pyramid, prism etc.)
Can anyone recommend books that deal with geometric bodies (cube, pyramid, prism etc.)?
I haven't been able to find any.
5
votes
4answers
175 views
I need a lot of questions for mathematics. Algebra to calculus so that I learn by solving.
One huge problem I have with learning mathematics is that I have not got enough problems to solve, with answers. Is there a resource that I can get hundreds of mathematical questions, small questions, ...
0
votes
0answers
123 views
Suggestion of Books for MCQ
I'm preparing for a competitive exam for which I need to practice multiple choice questions (both of single and multiple correct type) on the following topics:
Linear Algebra;
Abstract Algebra;
...
3
votes
1answer
123 views
Prize for textbook aesthetics
When browsing through Alain Connes' textbook on Noncommutative Geometry, whose illustrations must have been conceived as true works of love, I was wondering if there is a recognized prize for ...
4
votes
1answer
125 views
Galois Theory Texts
What is a very comprehensive text regarding Galois Theory?
I'm about to take a course in Galois Theory this spring, and I usually like to complement my course texts with something more rigorous, ...
18
votes
3answers
672 views
phd qualifying exams
Where can I find phd qualifying exams questions.Is there any website that keeps a collection of such problems?
I need it for doing some revision of the basic topics.I know of a book but that do not ...
2
votes
2answers
93 views
Any advise and suggestions about Real analysis and measure theory?
I am about to take a real analysis course and i wanna ask if anyone can provide some good texts or reference or any other source. The lectuer indeed suggested the Rudin real and complex analysis but i ...
2
votes
1answer
123 views
Problem Regarding Time Management
I don’t know whether it’s the right place to ask for such a request. I would like to express my apologies in advance if it anyhow goes against the dignity of the forum.
I’m taking preparation for a ...
