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18
votes
5answers
641 views

Is $3 \ge 1$ or is it just $3 > 1$?

Well, probably this might seem a really simple question (and it might be so too!), but off late me and my friends have been debating quite hard over this question. Is $3 \ge 1$ or is it just $3 ...
3
votes
4answers
167 views

Applications of logic

What are some applications of symbolic logic? I tried using Google and Bing but just got a bunch of book recommendations, and links to articles I did not understand.
7
votes
1answer
232 views

How to Remain Competetive at Mediocre University? [closed]

I am attending a university with a mediocre mathematics department. The courses at my school cover fewer topics and are less challenging than the same courses at top universities. How can I avoid ...
19
votes
7answers
2k views

Mathematical writing: why should we not use the phrase “we have that”?

In Knuth's Mathematical Writing, he writes on page 2, at number 8: Don't omit "that" when it helps the reader to parse the sentence. Bad: Assume $A$ is a group. Good: Assume ...
0
votes
1answer
146 views

Homogeneity Versus Heterogeneity in Student Groups

There is an overwhelming amount of research regarding homogeneous and heterogeneous grouping in education. The former refers to the practice of grouping "like" students together (regarding age, ...
4
votes
1answer
369 views

How impact the work of a pure mathematician in the society? [duplicate]

Firstable i explain my situation: On my University most of the careers are doing videos to explain what we do and try to atract more people to our careers. Im in a really bad position, because the ...
10
votes
1answer
808 views

Toddler introductions to higher mathematics

I bought my youngest (now 10 months old) "Introductory Calculus For Infants" by Omi Inouye a while back. It's actually an ABC book about the letter x and how no one ever plays with him until he meets ...
11
votes
3answers
6k views

Baby Rudin vs. Abbott

I am considering Stephen Abbott's Understanding Analysis and Walter Rudin's Principles of Mathematical Analysis. I am looking for a comparison between the two that addresses both of the following ...
4
votes
1answer
1k views

Self-studying through an undergraduate math course. Need Tao-like textbooks!

I'm a physics undergraduate student who always enjoyed math, and briefly studied it at a university but for various reasons (laziness, youth) gave up and changed 'majors'. But I always wanted to go ...
8
votes
1answer
673 views

The perception of mathematics

In my work I wrote the following sentence. "...there is a negative perception of mathematics and mathematicians, both within and outside of academia." Err. Right. So, I believe that this is ...
3
votes
3answers
471 views

Textbook Recommendation: Topological Dynamics

I need to take credits satisfying a topology requirement, and can structure it myself. My field of study is dynamical systems, can someone recommend a textbook that handles differential ...
9
votes
1answer
339 views

Journals or Magazines on Study Skills or How to Study Math

I am trying to find only journals or trustworthy magazines which can help math students to study math more efficiently and productively. I am not asking about books in this thread. In particular, I am ...
27
votes
4answers
2k views

Is mathematical history written by the victors?

The question is the title of a recent piece in the Notices of the American Mathematical Society, by twelve authors (of which I am one). The contention is that traditional history of mathematics is ...
1
vote
1answer
177 views

numerical linear algebra 101

since I'm a programmer and I need linear algebra, I'm starting considering how to teach myself a little of numerical linear algebra, not really optimize things right from the start, but I would like ...
6
votes
2answers
263 views

Why are square functions important in analysis?

I have been reading through chapter 1 of E.M. Stein's textbook Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals. In chapter 1, Stein discusses the relationship ...
4
votes
3answers
523 views

What's the motivation to add inner product and wedge product together in geometric product

I am reading some geometric algebra notes. They all started from some axioms. But I am still confused on the motivation to add inner product and wedge product together by defining $$ ab = a\cdot b + ...
10
votes
3answers
3k views

Preparing for Mathematics Olympiad

I am preparing for Mathematics Olympiad , can any one suggest me some books to prepare for olympiad ? The topics that usually come up involve: congruence modulo $n$, inequalities , number system, ...
0
votes
1answer
291 views

Manifold learning/nonlinear dimensionality reduction for beginners

I'm a computer science graduate student. I recently discovered manifold learning. I think I understand the very basic, high-level concept of nonlinear dimensionality reduction, but I'd like a ...
4
votes
1answer
108 views

Trustworthiness of foundational systems

Naively, we might think that if a foundations of mathematics is consistent, then its fair game. Then we learn a bit more, and we realize that even if a foundations of mathematics is consistent, it may ...
6
votes
2answers
143 views

Popular textbooks and current research.

I am sure that I will be finding out first hand as I am entering a PhD program, but I will ask my question anyway. Say, for instance, a student has worked through the majority of a textbook like ...
0
votes
1answer
49 views

What is the difference between “model” and “method”

I am not sure which forum to ask this question since the answer may change depending on the scientific area. I am analysing some time series using linear regression. I predict data using the linear ...
1
vote
3answers
94 views

The ubiquitous “helper function” $\frac{f(z) - f(a)}{z - a}$

I've been looking at basic complex analysis recently, and have noticed (am imagining?) something which I've never really paid attention to before: The "helper function" $$g(z) = \frac{f(z) - f(a)}{z ...
4
votes
2answers
199 views

How to determine the big questions in a field of mathematics?

During my self-study (and soon to continue at a university) of mathematics, one thing I have been interested in is how to to effectively learn the material. An answer to a question provided by ...
2
votes
1answer
185 views

Topology and commutative algebra.

I don't know both of these subjects, but I was wondering if there was any topology in commutative algebra. I don't need any detailed answer (since I don't know any of them yet)...So would it be ...
1
vote
1answer
104 views

What sections should I study to prove that fifth (and up) degree polynomial equations are not solvable with Fraleigh?

I'm Korean high school student who wants to study how to prove that degree ≥5 polynomial equations are not solvable. I know some of Set Theory and will study abstract algebra with 'A First Course in ...
0
votes
3answers
210 views

Does difficulty in math tend to shift over to the actual concepts? [closed]

So far (calculus 1), the math concepts that I learned have been pretty easy, and the greater difficulty is usually in solving certain problems. However, as you go higher and higher do the concepts ...
2
votes
4answers
3k views

How do you make less mistakes in math? [duplicate]

How do you make less mistakes in math? Do you try to be more alert, do you take your time more, or what? Usually I don't make that many mistakes, but sometimes (like now) I do math as I imagine I ...
5
votes
1answer
905 views

what is the best book to study contour integration?

what is the best book or website to study contour integration ? I find in some question answer using contour integration but I can't understand how they do that so is there any help ?
14
votes
4answers
3k views

mathematical maturity

So, I finished my undergrad with a degree in applied mathematics, but when reading some graduate level texts and/or papers, I often find myself struggling. I eventually get there, but I often feel ...
4
votes
2answers
260 views

Textbook Questions to Do while Self-learning

I am working through Dummit and Foote's Abstract Algebra this summer in preparation for a class next year. However, this is my first time really trying to learn a subject through only a text. It seems ...
38
votes
3answers
8k views

A path to truly understanding probability and statistics

I'm embarrassed to say that I have a PhD and hold an asst professorship, but get tripped up when reading statistics research. I am in a field of Business that is similar to IO Psychology or Social ...
9
votes
7answers
747 views

Advice on self study of category theory

I'm very intrested in start to study category theory with aim to use this in algebraic geometry. I already took courses (besides the basics) on commutative algebra and general topology with a soft ...
2
votes
0answers
54 views

Is this slightly different proof to Hibert's Theorem “different enough”?

I generally try and think up slightly different proofs to the material that I read in order to grasp some deeper possible insight, and then painstakingly record them in a latex document. I've been ...
2
votes
2answers
311 views

I am going to learn these math topics , please suggest me where to start?

I always did poor in mathematics and i even quit my mathematics from 10th grade but since I was good in programming ( C++ and Java) I took course related to computers in my college where I am going to ...
2
votes
0answers
161 views

Symbol for functions that vanish on boundary?

If I have a domain $ M \subset \mathbb{R}^n $, is there a standard symbol for the set of functions $ f \in C^\infty(M) $ that vanish on $ \partial M$ ? I feel like I have seen this before, but I'm ...
7
votes
2answers
350 views

self studying advice on analysis

I am trying to learn analysis on my own but there are times when I can't solve the problem or I get the solution wrong after looking it up, but I will only look up the problems online after I am ...
14
votes
1answer
330 views

Anecdote about mathematicians leaping to tops of problems and then building a staircase down?

I've run across this cute little story before, and now for the life of me I can't find it anywhere. It goes something like: Two people are looking out onto a mathematical landscape, and there are ...
4
votes
1answer
212 views

Learning Complex Analysis: Integrals vs. Power Series - ordering the development of results.

Over the last few months, I have been visiting elementary complex analysis. My exposure to complex analysis is pretty much limited to the material in three books: Ahlfors, Bak/Newman, and ...
14
votes
5answers
1k views

Favourite applications of the Nakayama Lemma

Inspired by a recent question on the nilradical of an absolutely flat ring, what are some of your favourite applications of the Nakayama Lemma? It would be good if you outlined a proof for the result ...
1
vote
2answers
114 views

Approximation of differential equations

Can someone provide me a good reference about approximation techniques in continous domain (not piecewise nor numerical methods) for differential equations?
2
votes
1answer
252 views

Convergence w.p. 1 vs convergence in probability: a “physical” example

I understand (proved) that convergence with probability one implies convergence in probability, and that the latter notion is indeed weaker; I've completed an exercise showing that a sequence of ...
10
votes
1answer
815 views

Special cases of the Stark-Heegner theorem with simple proofs

The Stark-Heegner theorem states that the ring of integers of the quadratic number field $\mathbb Q(\sqrt{m})$, where $m$ is a squarefree negative integer, is a principal ideal domain, iff ...
2
votes
2answers
384 views

Is the intersection of every non-empty family of inductive sets equal to the intersection of every inductive set?

In Halmos Naive set theory, there is the following passage (excuse my french) in his section introducing natural numbers : In this language the axiom of infinity simply says that there exists a ...
7
votes
4answers
290 views

Mathematical news sources.

I'm studying my high school right now but I really like math and it would be great for me if I could find a place where I can find about what is going on in the math world nowadays. About a year ago I ...
3
votes
1answer
100 views

Software for Binary Integer Linear Programs

I am aware that there is good software out there to solve integer linear programs (ILPs). However, is there (preferably free or low cost) software I could use to solve large binary integer linear ...
12
votes
3answers
1k views

How to go About Undergraduate Research

I apologize in advance if this question is out of the scope or focus here. I was just wondering about the whole prospect of researching as an undergraduate. How to do it? Who to talk to in my ...
5
votes
2answers
145 views

Why do we only consider quadratic domains as Euclidean domains with squarefree integers?

I have been reading "Introductory algebraic number theory" by Alaca and Williams, and in the opening chapters they use the quadratic domains $\mathbb{Z}+\mathbb{z}(\sqrt{m})$ for non-square $m$ and ...
3
votes
0answers
99 views

How to get interest in the mathematics of tax

In a similar vein to my previous thread, I will also be teaching about the mathematics behind taxation - to a lot of people, this is very mundane - but that is not true of everyone. The practicality ...
3
votes
2answers
771 views

Examples of applications of Linear differential equations to physics.

I wonder which other real life applications do exist for linear differential equations, besides harmonic oscillators and pendulums. I'm looking for examples to include in a document that talks about ...
6
votes
2answers
217 views

The notations change as we grow up

In school life we were taught that $<$ and $>$ are strict inequalities while $\ge$ and $\le$ aren't. We were also taught that $\subset$ was strict containment but. $\subseteq$ wasn't. My ...