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2
votes
3answers
302 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 + ...
0
votes
1answer
193 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
100 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 ...
7
votes
2answers
125 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
32 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
86 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
170 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
103 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
90 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
197 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
566 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 ...
2
votes
1answer
283 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 ?
11
votes
4answers
982 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 ...
3
votes
2answers
185 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 ...
35
votes
3answers
2k 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 ...
8
votes
7answers
405 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 ...
0
votes
0answers
52 views

What math publications are re-publishable?

If I wanted to make a math theory database, what sources could my users freely take from? What if they re-expressed a theorem in another way?
2
votes
0answers
49 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
215 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
94 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
254 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 ...
11
votes
0answers
261 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
161 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 ...
13
votes
5answers
553 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 ...
4
votes
0answers
749 views

Is Arthur Engel's Problem Solving Strategies too advanced for a beginner in Olympiad mathematics? [closed]

I am having lots of problems solving Arthur Engel's text. While not all the stuff goes over my head, a major portion of it does. Even some of the solved examples are beyond me. I have never ever done ...
1
vote
2answers
102 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
98 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 ...
3
votes
0answers
105 views

The Psychology of Math and Logic [closed]

I frequently hear comments from people to the effect that "Studies have shown that students who take (intro) logic courses don't show any signs of improvement in logical/rational/critical thinking." ...
9
votes
1answer
690 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
201 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
238 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 ...
2
votes
1answer
69 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 ...
11
votes
3answers
532 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 ...
10
votes
0answers
515 views

Are there “mental calculator” persons that can recognize closed-form expressions?

There are people, sometimes called mental calculators, who is capable of performing fast calculations in their head, involving multiplication, factorization, finding logarithms and roots of a high ...
3
votes
2answers
95 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
88 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
279 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
202 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 ...
11
votes
2answers
1k views

Relearning from the basics to Calculus and beyond.

Assume someone has very limited knowledge of math. (low level high school, 5-6 years ago) How would they learn from the basics of algebra, geometry and trigonometry to a solid foundation for calculus ...
5
votes
2answers
116 views

State-of-art of the Discrete Fourier Transform

I would like to know what is the state-of-art in the research of the discrete Fourier transform. I have listed some questions to help answering, please add your own to make the list more ...
3
votes
1answer
202 views

What's correspondence between the model theoric and the set theoric kernel of homomorphism?

A kernel of a mapping $h$ from $\mathfrak{A}$ to $\mathfrak{B}$, generally, is an equivalence relation $\{(a,a') \in \mathfrak{A} \times \mathfrak{A} \mid h(a)=h(a')\}$. However, in model theory, ...
8
votes
1answer
187 views

Construction(s) of new integral domains from “old ones”

Given an integral domain $D$, there are several ways how to construct a new integral domain related to D. For example, one can consider a ring of polynomials/formal power series/formal Laurent series ...
7
votes
1answer
186 views

Motivation for Jordan Canonical Form

I took linear algebra and understood the proof that linear operators on a vector space over an algebraically closed field have a Jordan Canonical Form. Why should I care about this theorem? I ...
2
votes
4answers
311 views

Resources for learning mathematics for intelligent people?

Could people recommend resources to help my wife learn more complicated mathematics? She had a really terrible maths education, and while she essentially OK with every day maths she keeps wanting to ...
3
votes
2answers
126 views

What's the correct name in english for “Analysis in $\Bbb R^n$”?

Well, this question may seem silly and I fear it's even out of topic here. My motivation to ask that is to know the correct terminology when talking about that here in Math.SE. The point is, here in ...
6
votes
1answer
178 views

Is there an integral form of Newton's method?

Warning : This seems like a silly sort of question, not the kind I'd ask out loud. The contraction mapping theorem is a basic tool for proving existence of, and finding solutions to, equations. Given ...
1
vote
2answers
225 views

What programming languages are used in (chaotic) dynamical systems and nonlinear phenomena research?

I'm currently considering pursuing postgraduate studies in the field of chaos/dynamical systems/nonlinear phenomena, and was wondering whether there are particular programming languages that are ...
6
votes
2answers
90 views

Usefulness of induced representations.

I am learning representation theory from Serre's book by myself. Currently I am reading about induced representations, but I don't understand the importance. The concept looks strange and the ...
8
votes
2answers
196 views

Ideas for a present to my topology teacher

Tomorrow is the my final lecture in my favorite course, algebraic topology. I want to give a present to my prof. as a keepsake, something along the lines of this only something I can make due ...
4
votes
3answers
474 views

Books for a beginner

I am a student of 11th grade and i have completed the syallabus of both 11th and 12th grade maths with complete understanding and it was possible coz of the love for this subject that i have. I don't ...