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-1
votes
0answers
17 views

Bayesian Theory: Is it doable from $0$?

How hard is Bayesian Theory? It is listed as a postgraduate course (I'm an undergrad), I haven't done much stats (only a bit of likelihood and liner regression). Is it possible to learn and do it as ...
3
votes
0answers
40 views

Are there any proofs that only exist by induction?

I've come to learn more about induction recently for proving things, and one thing stands out to me. It seems like you could just data-mine patterns and guess a relationship you think might be ...
10
votes
5answers
3k views

Mathematics, Philosophy and writing.

Do you know of any famous mathematicians who were also philosophers? I have heard of Descartes, Plato and Leibniz. Are there other good examples, especially more modern examples? Also welcome are ...
0
votes
0answers
35 views

Intuition regarding $\lim \lVert u_r - u \rVert_{p}=0$

I have some trouble intrepreting the following statment If $u$ is harmonic in $D$ and has bouned means for order p on circles of radius $< 1$ then $\lVert u \rVert_{p}=\lVert u \rVert_{L^{p}}$ ...
24
votes
2answers
268 views

Origins of Differential Geometry and the Notion of Manifold

The title can potentially lend itself to a very broad discussion, so I'll try to narrow this post down to a few specific questions. I've been studying differential geometry and manifold theory a ...
3
votes
1answer
125 views

Are there any modern mathematicians whose research interest is in “Probability Theory”? [closed]

I have seen professors in universities list "stochastic calculus", "stochastic analysis", "stochastic processes", "stochastic geometry" and "applied probability" as research interests, but are there ...
31
votes
6answers
5k views

What are some interpretations of Von Neumann's quote?

John Von Neumann once said to Felix Smith, "Young man, in mathematics you don't understand things. You just get used to them." This was a response to Smith's fear about the method of characteristics. ...
4
votes
0answers
106 views

On comparing two different notions of compactly generated space

I have encountered, in different circumstances, the following two slightly different categories: The full category of $\mathsf{Top}$ consisting of all objects that are: a) topological spaces ...
11
votes
4answers
2k views

Topics on Number theory for undergraduate to do a project [closed]

Im an undergraduate in the mathematics field ..So i wanna be alittle more productive and wanted to do an essay or project mostly on number theory or Algebra(Rings or Groups) and i want to ask if you ...
4
votes
6answers
3k views

Applications of Complex Numbers

For my Complex Analysis course, we are to look up applications of Complex Numbers in the real world. The semester has just started and I am still new to the complex field. I want to get a head start ...
14
votes
3answers
2k views

Does writing a bachelor thesis make sense?

I am a math student in my fourth semester. At my university, it is common to write a bachelor-thesis in the end of the bachelor program in almost all subjects while in the math undergraduate program ...
2
votes
1answer
97 views

How do you use reference books?

Reference books at the research levels often does not include any problem or exercise. While you can't read these books like novels(you normally need to work on other sheet of paper), I'm just ...
6
votes
1answer
316 views

Recommended research topics for high school student

I am a high school senior and I am interested in doing a math research. I hope someone can recommend areas or topics of research that are challenging, rewarding, and yet do not exceed my capability. (...
23
votes
11answers
3k views

Gap year to study math

This is a plan in its earliest and thus least concise stage, so either bear with me or don't read the following babble (I bolded some of the important stuff): I am a high school graduate who is about ...
48
votes
6answers
10k views

What is mathematical research like?

I'm planning on applying for a math research program over the summer, but I'm slightly nervous about it just because the name math research sounds strange to me. What does math research entail exactly?...
-3
votes
2answers
52 views

Redundant proof in Math paper [on hold]

Recently, I read a published math paper and I found that in the excessive argument in the proof of one of its theorem. In fact, in my opinion, the redundant part is not even correct, because it ...
2
votes
1answer
110 views

Undergraduate Project Suggestions

A student of mine has expressed interest in doing an independent project next quarter with me. This would not be for credit and it is purely for her own educational stimulation. She wants to study ...
25
votes
2answers
1k views

Collections of undergraduate research projects [closed]

I would like to compile a "big list" of undergraduate research projects in the following areas of mathematics: calculus; analysis; abstract algebra; linear algebra; number theory; geometry; ...
0
votes
1answer
126 views

Researching in Mathematics [closed]

I am presently pursuing Engineering, but I want to make my career in the field of mathematics. How do I come to know of the specific topic in math in which I would like to research, in which I would ...
1
vote
0answers
42 views

Error Correcting Code and Graph Theory

I am currently in an introductory graph theory class, and we are supposed to give a short presentation by the end of the semester. Recently, I've learned (a very small amount) about error correcting ...
18
votes
4answers
618 views

Problems from the Kourovka Notebook that undergraduate students can fully appreciate

The Kourovka Notebook is a collection of open problems in Group Theory. My question is: could you point out some (a "big-list" of) problems [by referencing them] presented in this book that are, ...
0
votes
0answers
22 views

Calculus for Proving Properties of Discrete Objects

I posted a question earlier about a proof in graph theory I was trying to figure out. In my attempt I used Calculus to prove a part of the theorem. In the comments people kept saying how you shouldn't ...
-1
votes
0answers
36 views

Advice on Research topics in Linear Algebra [on hold]

I am a rising senior undergraduate student. I have taken following courses and I have an opportunity to do a project in Applied Linear Algebra at a fairly good Mathematics department. I am trying to ...
9
votes
0answers
184 views

How can I begin reading journals and papers?

I am an undergraduate CS student but I love Math and spend most of my time doing and reading Maths books. I realise that it's important to get into the habit of reading papers and journals so it will ...
1
vote
1answer
95 views

Pure mathematics research [closed]

What can a first year mathematics undergraduate, who wants to pursue research in pure mathematics, learn in 67 days that will help him in the future?
6
votes
3answers
1k views

How to stay academically active during a Mathematics Gap Year? [closed]

This year I started at the University of Cambridge to study Maths. I was very unfortunate to contract a serious infection early on in the term, and as a reult it has been mutually decided between ...
1
vote
5answers
2k views

What really is an indeterminate form?

We can apply l’Hôpital’s Rule to the indeterminate quotients $ \dfrac{0}{0} $ and $ \dfrac{\infty}{\infty} $, but why can’t we directly apply it to the indeterminate difference $ \infty - \infty $ or ...
1
vote
0answers
20 views

Style guide/typeface for handwritten mathematics

When writing math on graph paper, it's a small struggle to make my work as legible as possible and also use the page as efficiently as possible. I've read a little online about how latex typesets, ...
1
vote
0answers
16 views

Probabilistic Method/Model for Traffic Flow

Context: Given a network system or a traffic system with some value related to the system. Question: Which probabilistic methods, model, distributions are used frequently to predict a event (for ...
1
vote
1answer
35 views

Suggest books on Combinatorial Graph Theory

I am going to start self-studying Combinatorial Graph Theory. Kindly suggest books or study materials available online. I have been told that it is basically application of linear algebra, mainly ...
-3
votes
1answer
58 views

Simple examples for motivation of topology [on hold]

It is easy to see motivation for groups and fields, as abstractions of operations defined on integers, rationals, reals etc. and how the results from those abstractions apply to integers, reals etc. ...
3
votes
3answers
40 views

What is the proper usage of $f: X \to Y$ and $f: \mathcal{P}(X) \to \mathcal{P}(Y)$ in proof writing.

I have read somewhere that suppose we are given a $$f: X \to Y$$ then $f$ is further associated with $$f: \mathcal{P}(X) \to \mathcal{P}(Y)$$ Does "associated" here means extended to a set valued ...
0
votes
0answers
24 views

What are interesting functions in 2D that vary visually as compositionality increases?

I wanted to create a function that its shape was a function of the depth of the compositionality (on a fixed interval). For example consider some compositional function $$f(x_1, x_2) = g( g( g( h_1(...
3
votes
1answer
68 views

Writing Math: Is using both $e^x$ and $\exp(x)$ ok for longer works?

I wanted to know what you guys think about mixing both notations for the exponential function $e^x$(for simple argument and to save space for larger equations) and $\exp(x)$ (for more complicated ...
1
vote
1answer
69 views

Does anyone know a no-nonsense intro to “logic for mathematics” that I can give to a Year 11 student?

I'm looking for material on propositional and first-order logic to give to a Year 11 student that explains how they're used "in practice." For example, I want to be able to write the null-factor law ...
8
votes
2answers
258 views

Explaining Mathematical Modelling to a nonmathematician

Due to the interdisciplinary nature of my project, I find myself collaborating a lot with nonmathematicians especially biologists, medical doctors, etc. I work mostly on mathematical models as applied ...
3
votes
0answers
85 views

What is the point of making dx an infinitesimal hyperreal?

It seems fairly common to describe $\mathrm{d}x$ in nonstandard analysis as an infinitesimal. But after thinking it through (and then skimming Keisler's text), I can't see the point and actually think ...
2
votes
0answers
44 views

Overly advanced techniques in simple questions: trouble in exams?

I have yet to ascend to the heights of university education, and before I do, I would like to clear something up: As I was revisiting a book on complex analysis, I see questions like the following: ...
2
votes
2answers
74 views

Simple question: Which is the Wikipedia definition of axiom of choice

I looked up Wikipedia, and on the top of the page it says: For every indexed family $(S_i)_{i \in I}$ of nonempty sets, there exists an indexed family $(x_i)_{i \in I}$ of elements such that $...
0
votes
1answer
41 views

What subbase generates metric topology?

Let metric topology be the topology generated by metric balls of a metrizable space $X$ Is there a subbase $S$ that generates the metric topology? I am asking because in most textbooks, it seems ...
45
votes
5answers
8k views

What are the work habits of the best mathematicians? [closed]

How hard did Gauss, Euler, Einstein,..., and so on work? How many hours were they spending learning and or thinking about their studies? Do the "best" mathematicians (or scientists) share many similar ...
1
vote
0answers
40 views

Motivation of indices of all subgroups of symmetric group $S_n$

In 1858 a prize question of the Acad´emie des Sciences was - What are the indices of all subgroups of symmetric group $S_n$ acting on $n$ objects ? Three submissions was submitted in 1860, no ...
14
votes
4answers
779 views

Has error correction been “solved”?

I recently came across Dan Piponi's blog post An End to Coding Theory and it left me very confused. The relevant portion is: But in the sixties Robert Gallager looked at generating random sparse ...
2
votes
1answer
30 views
+50

Upper bound for the no. of maximal ideals of a finite commutative ring ( with unity ) in terms of the order of the ring and/or its number of units?

Is there any known upper bound for the no. of maximal ideals of a finite commutative ring ( with unity ) of order $n$ , in terms of $n$ and /or in terms of the no. of units of the ring ? Say , does ...
1
vote
3answers
168 views

Virtues of Presentation of FO Logic in Kleene's Mathematical Logic

I refer to Stephen Cole Kleene, Mathematical Logic (1967 - Dover reprint : 2002). What are the "pedagogical benefits" (if any) of the presentation chosen by Kleene, mixing Natural Deduction and ...
1
vote
0answers
169 views

Why would I learn modern category theory if my interest mainly is structured sets, what would I have to gain? [closed]

A long time ago I studied mathematics at the University of Stockholm. I had a romantic view of modern algebra and manage to make the first two algebra courses by self studies in order to immediately ...
45
votes
25answers
4k views

What books should I get to self study beyond Calculus for someone about to start undergrad mathematics?

I am struggling to pick out books when it comes to self studying math beyond Calculus. My situation is as follows. I have taken all math courses at my school (up to Calc BC and AP Stats) and I have ...
8
votes
7answers
507 views

Mathematics and Perfectionism? [on hold]

Background I am an undergraduate and I have just finished my first calculus class (Calc I) this summer. While this class has gone very well for me by any objective standard, I find myself drifting ...
239
votes
30answers
18k views

A challenge by R. P. Feynman: give counter-intuitive theorems that can be translated into everyday language

The following is a quote from Surely you're joking, Mr. Feynman . The question is: are there any interesting theorems that you think would be a good example to tell Richard Feynman, as an answer to ...
1
vote
2answers
46 views

How was statistics formulated [on hold]

I'm sorry for the naive question, but I've only been taught statistics at a high school level (extremely basic) and it always remained a mystery as to how certain concepts in statistics existed (...