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4
votes
1answer
57 views

Analytic solutions to a simple math trick

As proven here $3816547290$ is the only positive integer in which every digit is used; each digit is used only once; the first $n$ digits are divisible by $n$, for $n=1,...,10$. ...
14
votes
7answers
383 views

What are some mathematically productive ways to waste time? [on hold]

What are some productive things that can be done (other than directly studying Mathematics) during leisure time that has a side effect to improve oneself at Mathematics? For example, reading ...
6
votes
4answers
107 views

Math newbie: what to read? [on hold]

Quick question for you all: what should a high school senior who intends to major in CS and math read to become familiar with proofs, calc, algorithms, etc? I know that's incredibly broad, basically ...
2
votes
1answer
35 views

Counting in other bases [duplicate]

While this could be considered opinionated to a certain degree, by setting the requirement as ease of use, is there a base that is better for performing simple math functions (+-×÷) than base ten. ...
2
votes
3answers
87 views

A mathematically mature introduction to Turing Machines and Computability [reference-request]

In the computer science course for mathematicians held at my university Turing Machines have been presented very briefly. So much so that I didn't quite get why they are relevant to mathematics. I did ...
6
votes
3answers
117 views

Lang's Linear Algebra: what's next?

I've completed the study of Lang's Linear Algebra ($3^\text{rd}$ edition). To put it simply, I have enjoyed the subject and I would like to know "what's next". In other words, I would like to know ...
4
votes
2answers
93 views

Probabilistic techniques, methods, and ideas in (“undergraduate”) real analysis

As the book Probabilistic Techniques in Analysis by Richard Bass shows, nowadays techniques drawn from probability are used to tackle problems in analysis. The mentioned book presents a survey of ...
1
vote
0answers
33 views

Looking for a partial converse of Rolle's theorem

Let $f: [a,b] \to \mathbb R $ be a continuous function differentiable in $(a,b)$ such that $f(b)=0$ and for some $c \in (a,b) , f'(c)=0$ ; then under what additional conditions can we conclude that ...
0
votes
0answers
32 views

Some questions about prime divisors and no. of primes

Let for an integer $n \ge 2$ , $\omega (n)$ denote the no. of distinct prime divisors of $n$ and $\pi (n) $ be number of primes not exceeding $n$. Let $a_1,...,a_k$ be integers greater than $1$ and ...
1
vote
1answer
57 views

Book comparison, Linear Algebra

so next semester (Spring 2015) I'm taking a Linear Algebra class. I was wondering if anyone who's had this book "Linear Algebra and Its Applications, 4th Edition - by David C. Lay" can give me an ...
14
votes
4answers
1k views

Why do we need to learn Set Theory?

I was planning to write some article for the Mathematics magazine of our college and it occurred to me that it will be a good idea to write about the impact and importance of Set Theory. I plan ...
1
vote
0answers
15 views

Ability to View Answers in LaTex [migrated]

Is there an option or can one be implemented so that new users like myself can view the "source code" of others answers. Obviously there are many tutorials in which we can find the correct commands, ...
0
votes
1answer
22 views

Restriction estimates

What is the defining property of what someone in the harmonic analysis community would call a "restriction estimate?" I see sobolev norms, Fourier transforms, and inequalities relating these. The ...
0
votes
0answers
23 views

Permutations and combinations - fun questions [on hold]

Well I am studying permutations and combinations, and I'm finding it quite an interesting topic. Surprisingly enough, it seems to have practical applications. I was looking for some questions on the ...
0
votes
0answers
30 views

On subgroups of the form $HZ(G)$ where $H$ is abelian subgroup of non-abelian group $G$ such that $H \rlap{\;\,/}\subseteq Z(G)$

Let $H$ be a an abelian subgroup of a non-abelian group $G$ such that $H \rlap{\;\,/}\subseteq Z(G) Z(G)$ ; then I can prove that $HZ(G)$ is an abelian subgroup such that $Z(G) \subset HZ(G) \subset ...
1
vote
2answers
42 views

Is there a good short phrase for a point where a function is continuous but not smooth?

Given a point $x_0$ where a function $f$ is $C^0$ but not $C^1$, how could one call this point intuitively? I am not looking for a technically precise term (like a point where $f'$ is ...
0
votes
1answer
59 views

math books of undergraduate/graduate level without formula? [on hold]

Just wondering, is there a math book talks deep into the math ideas (maybe undergraduate or graduate level, so not the pre-algebra content), but comes with no or very few formula?
21
votes
20answers
2k views

What are some interesting sole exceptions or counterexamples? [duplicate]

Many theorems assert that a particular property holds for all objects in a class except those in a given list of exceptions. Examples of rules that admit precisely one exception include: All primes ...
2
votes
0answers
110 views

Can anyone explain this quote about how mathematicians think?

I found this quote by Stephen Wolfram on page 1177 of his book A New Kind of Science. Yet of the limited set of people exposed to higher mathematics, different ones often seem to think in ...
-4
votes
0answers
52 views

Give an example of a field K, an extension field F, a subring R of F containing K where R is not a field? [on hold]

Give an example of a field K, an extension field F, a subring R of F containing K where R is not a field? I had $\mathbb{C}$ as a field, $\mathbb{C}(x)$ as a field extension, and $\mathbb{C}[x]$ ...
0
votes
0answers
49 views

What is some reason that there are no book bridge the gap of these three books

I am referring to the (beginner's text- Stochastic Calculus by Mircea Grigoriu and Introduction to Stochastic Calculus by klebaner.) and the advanced texts - stochastic differential equation by ...
1
vote
0answers
50 views

Physical or geometric meaning of the trace of a matrix

The geometric meaning of the determinant of a matrix as an area or a volume is dealt with in many textbooks. However, I don't know if the trace of a matrix has a geometric meaning too. Is there ...
3
votes
1answer
42 views

What is the discrete log used for?

Perusing Wikipedia, I stumbled on the discrete logarithm. I looks interesting that we'd be able have a function that could solve $b^k=g$ for integers $b,k,$ and $g$. However, Wikipedia says "No ...
1
vote
1answer
69 views

subtle/annoying fallacious proofs [duplicate]

I've been invited to a maths themed Xmas after party. I need to prepare a selection of interesting, and relatively simple fallacious proofs which other guests will try and find the flaw in. I'm trying ...
9
votes
2answers
121 views

How to select the right books?

As the saying goes, "Give a man a fish, feed him for a day. Teach a man how to fish, feed him for life." I've always had a problem with selecting appropriate books. It could be a problem that I'm a ...
1
vote
0answers
40 views

Motivation for Putnam (soft question)

This question may be too specific and too vague. But I'm curious about this. How highly are the applicants evaluated in PhD admission if they were ranked above the cutoff of honorable-mention in ...
6
votes
0answers
73 views

Examples of useful, insightful, and interesting hand-waving

I am really amused by the answers to this question on "Most harmful heuristic" posed on MathOverflow, from which I've benefited a lot. However, it seems to me that some hand-waving may be really ...
6
votes
2answers
109 views

How to explain to a layman why Fermat's Last Theorem involves non-trivial math?

Fermat's Last Theorem states, given$$x^n + y^n = z^n$$ no three integers $x,y,z$ will satisfy the equation given integer value of $n$ greater than two. On the surface this seems like something that ...
3
votes
1answer
58 views

Which courses should I take to prepare for PHD in Finance/Econ/OR

Since it's finally the end of the year, I would like to gain some insights about which course should I take that are most helpful to prepare for application to the PHD program in Finance/Financial ...
17
votes
0answers
186 views
+50

Effective Research Notes

Note-taking for research is vital to your success as a mathematician. As I look back at some of my handwritten notes, I realized how poor they were. I had thought to myself, "What happened?" I was ...
8
votes
5answers
147 views

Sources for mathematics outside the mathematics world

In this question I would like to ask you about material showing the uses (or occurrences) of mathematics in the everyday world. The aim is to encourage with it a group of young undergraduate ...
2
votes
1answer
130 views

Why is the axiom of choice not taught from the start to mathematics undergraduates?

I've recently discovered that the following theorems require the axiom of choice to be proven: every surjective function has a right inverse. a real-valued function that is sequentially continuous ...
5
votes
0answers
20 views

Discrete analogue of Green's theorem

Following formula concerning finite differences is in a way a discrete analogue of the fundamental theorem of calculus: $$\sum_{n=a}^b \Delta f(n) = f(b+1) - f(a) $$ We can think about the Green's ...
1
vote
2answers
54 views

Probabilistic implications of the existence of non-measurable sets

Measure theory and probability theory are deeply connected through the interpretation of subset measures on the sample space as probabilities of events. A major (and somewhat disturbing) result from ...
3
votes
0answers
40 views

Why is the slope-intercept form of the equation of a line often written $y=mx+b$? Why $m$ instead of $a$?

After a quick google search, I read something about Conway suggesting the $m$ having to do with "modulus" ... This seems odd to me, but perhaps there is some mathematical reason? I've heard of the ...
-1
votes
0answers
42 views

List of simple, common functions with an incomplete domain or range on $\mathbb{C}$

This may seem like a strange question, but it's an interest of mine and I would appreciate the help of the community in addition to brainstorming on my own. As the question states, I'm looking for ...
4
votes
1answer
59 views

Is there a “unifying framework” for harmonic analysis?

Recently, I was exposed to a basic harmonic analysis course. Although the course is almost over, I still can't put my finger on what harmonic analysis is about. I have a vague idea that it is ...
1
vote
2answers
56 views

Self-Learning Geometry

I'm an undergraduate senior wondering where he should start in learning geometry. My university unfortunately offers no such course. Should i begin with riemann geometry or differential geometry and ...
0
votes
1answer
39 views

Probability in a Magical World

We know the frequentist definition of probability-the probability $p$ of an event $E$ is the limiting frequency the event happens when the associated random experiment is repeated large number of ...
1
vote
1answer
32 views

Request for Recommendation of a Handbook of pure Mathematics

I am looking for some books at undergrad level that give a good pedagogical coverage of of topics like topology,group theory,analysis,measure theory and probability with a nice exposition.Even books ...
6
votes
1answer
65 views

What level of math is needed to learn fractional calculus?

I was skimming through wikipedia pages and stumbled upon the fractional calculus page. My interest increased when I noticed it has applications in physics. I was wondering as an undergraduate who's ...
3
votes
1answer
31 views

Prerequisites for Hartshorne: Euclid and beyond?

as the title suggests, I am looking for the prerequisites to Hartshorne's Euclid and beyond. I just found this book and I think it's wonderful, but the downside is that I only know math up to single ...
-6
votes
0answers
39 views

study question master math [closed]

How to master advanced mathematics ? Do you think that with hard work and quasi-absolute determination one can achieve that ? Thank you
6
votes
2answers
330 views

How can I pick up analysis quickly?

I have a 2-3 week recess from university for winter break. In this time, I would like to learn analysis, starting with Walter Rudin's Principles of Mathematical Analysis, and then, if at all possible, ...
1
vote
1answer
56 views

Book recommendations for topics leading upto Algebraic geometry

I'm interesting in studying algebraic geometry (specifically either from Shafarevich or Hartshorne). Assuming a high school and basic college math education, what should be the topics and the order ...
2
votes
1answer
64 views

Homotopy Type Theory prerequisites.

I've done some undergraduate level study of algebraic topology (most Hatcher's book) and the smallest amount of type theory in a foundations of mathematics course. Homotopy type theory sounds amazing ...
0
votes
1answer
55 views

Question about independent study in differential geometry for an undergraduate.

I am a senior undergraduate math and physics student applying to graduate school in math for this upcoming fall. I have had classes in: Abstract Algebra (Rings, Fields, and Groups), Point-Set ...
0
votes
0answers
25 views

Learning Stochastic Processing, Modeling, and Analysis: Any Available Workbooks?

Motivation behind the question: I took the upper-level probability course at my college, and did pretty well. Most of the time throughout the class, I found myself intuitively understanding the ...
0
votes
0answers
40 views

Order of study? Rudin, Spivak, Munkres?

I'm currently taking an analysis course at a top 10 four year university in which we use Baby Rudin as our primary text. I was curious to know the order in which I should continue my studies. That ...
7
votes
0answers
95 views

How to listen math lectures?

Many times, the lectures goes beyond the head and not easy to follow, (at least with me),mainly in the workshop/conferences, though the audience are eager to learn something from it. Also, most of ...