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2
votes
1answer
101 views

What is the difference in chance, based on foreknowledge of the resolution?

I'm working to understand the differences between Odds, Probability and Chance. I've come up with a hypothetical situation to show where I'm having a bit of an issue. Chad shuffles a standard deck ...
4
votes
2answers
3k 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?
5
votes
2answers
770 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 ...
2
votes
1answer
886 views

Quadratic ODE systems

Linear ODE systems $x'=Ax$ are well understood. Suppose I have a quadratic ODE system where each component satisfies $x_i'=x^T A_i x$ for given matrix $A_i$. What resources, textbooks or papers, are ...
6
votes
5answers
1k views

What exactly is “approximation”?

There are a lot of great "approximations" that exist in the mathematical field:$$\dfrac{22}{7} \approx \pi$$ $$e \approx \left(1 + \dfrac{1}{n}\right)^n$$But the fact that I have yet to know what ...
4
votes
0answers
99 views

what's special about $\frac{1}{x}$ among other powers? [duplicate]

Possible Duplicate: What is so special about $\alpha=-1$ in the integral of $x^\alpha$? We all know the rule to find primitives (=antiderivatives) of powers of $x$: $$ \int x^\alpha dx = ...
1
vote
2answers
195 views

Learning patterns and the maths

I am interested in learning more about patterns. My objective is to learn about how to analyse a set of numbers (not infinite but a large set of numbers in sequence) and see the patterns and then ...
4
votes
0answers
107 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.
10
votes
2answers
322 views

Does there exist another way of obtaining a topological space from a metric space equally deserving of the term “canonical”?

Every metric space is associated with a topological space in a canonical way. According to this source, this amounts to a full functor from the category of metric spaces with continuous maps to the ...
4
votes
1answer
168 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 ...
6
votes
5answers
3k views

How does one begin to even write a proof?

I'm in my first proof based class and I'm just having a lot of trouble writing proofs. I mean I know it's not going to come natural and it will take time, but seroiusly, how does someone begin to ...
9
votes
1answer
138 views

Who are the most inspiring WOMEN communicators of math for a general audience?

This is a follow up to my earlier question. I'd like to improve the gender balance of my podcast series. (I interview people who are inspired by math and are inspiring others.) Through no conscious ...
52
votes
8answers
8k views

How much Math do you REALLY do in your job?

I am writing this, as I am a currently an intern at an aircraft manufactur. I am studying a mixture of engineering and applied math. During the semester I focussed on numerical courses and my applied ...
0
votes
1answer
115 views

Determining length of an “arc” drawn just below an another arc with known length by intuition

There is an arc a to b. The length is say 1 unit. There is an another arc c to d, drawn just below a to b, such that it sticks with it (ie. No vertical y space). Let us say i have my world ...
2
votes
1answer
66 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 ...
8
votes
5answers
3k views

How do you rebuild your Math skills after college? [closed]

I minored in Math in college (B.S. Software Engineering), and went through advanced Calc, Differential Equations, etc. But about 6 months after I graduated I had lost all my formulas. Now, about 5 ...
2
votes
1answer
4k views

Is mathematics considered a science [duplicate]

Possible Duplicate: what is the definition of Mathematics ? I would like to know if mathematics is considered a science? I've searched the internet and asked many people for insight to no ...
7
votes
1answer
594 views

Prerequisites for studying Hodge theory and the Hodge conjecture

To what branch of mathematics does the Hodge conjecture belong? I'm aware that it's very advanced, but what kind of prerequisites would one need to understand those problems? Can you suggest some good ...
4
votes
1answer
244 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 ...
3
votes
3answers
140 views

Equation in the real world

Does a quadratic equation like $x^2 - ax + y = 0$ describe anything in the real world? (I want to know, if there is something in the same way that $x^2$ is describing a square.)
2
votes
1answer
46 views

Applications of hypergeometric continued fractions

http://en.wikipedia.org/wiki/Gauss%27s_continued_fraction Using a technique due to Gauss a lot of special functions can be expressed as continued fractions. What applications of this are there ...
0
votes
1answer
33 views

How to obtain estimate of covariance matrix that will be guarantee to be semi-positive define?

How to obtain estimate of covariance matrix that will be guarantee to be semi-positive define ? (Is CrossValidated better place for this question ?)
1
vote
0answers
28 views

some reference for differential calculus of non-regular functions

could someone recommand some reference for differential calculus of non-regular functions? In particular, for the right-continuous functions of finite variation. Thanks a lot!
8
votes
9answers
1k views

what is the definition of Mathematics ? [closed]

we all study mathematics , and all of us learn mathematical methods to solve problems , we learn how to prove , how to think mathematically but the question is, what is mathematics ? how can we ...
56
votes
5answers
5k views

Is there any branch of Mathematics which has no applications in any other field or in real world?

Is there any branch of Mathematics which has no applications in any other field or in real world ? for instance , maybe : number theory ? mathematical logic ? is there something like this ?
8
votes
1answer
3k views

Simply Explain the General Number Field Sieve

As a beginner to the world of integer factorization, my idea of factoring an integer is to generate a large list of prime numbers below this number and to repeatedly try to divide the integer by these ...
2
votes
2answers
583 views

Uncertainty in mathematics

I have a solid (but not great) intermediate college experience in math, but now I've started exploring higher-level mathematics, out if curiosity. I was surprised that there's a lot more uncertainty ...
11
votes
4answers
676 views

How can I explain topology to my grandmother?

I was recently look at a post on tex.stackexchange about explaining $\LaTeX$ to the OP's grandmother. I was wondering, could the same thing be done for topology? Except in this case the "grandmother" ...
9
votes
2answers
3k views

Geometric intuition behind gradient, divergence and curl

I learned vector analysis and multivariate calculus about two years ago and right now I need to brush it up once again. So while trying to wrap my head around different terms and concepts in vector ...
7
votes
4answers
241 views

Why are homomorphisms usually assumed to be functions?

A group homomorphism is usually defined to be a function $\phi$ such that if $x * y = z$, then $\phi x \times \phi y = \phi z$. However, this can be generalized. We could define that a group ...
7
votes
1answer
248 views

Is it possible to avoid redundancy in a foundational work?

Imagine we're developing all of mathematics from scratch. We settle on using a set-theoretic foundation. Early on, we assert that an ordered pair $(x,y)$ can be abbreviated $xy$ whenever there is no ...
4
votes
5answers
1k views

Math vs Probability vs Statistics

For a certain job interview, I gave myself a 6 in SQL and 8 in Statistics. I love math and probability but I always found significance testing and confidence intervals rather dry. What is the ...
7
votes
1answer
134 views

Ultrafilters in Topology

I have seen the use of ultrafilters in topology to prove Tychonoff's theorem. In fact, this is the only application of ultrafilters in topology I have been able to find so far. Are there any other ...
0
votes
1answer
166 views

What other rules are there in mathematics?

I'm reading Conceptual Mathematics: A First Introduction to Categories. a set $A$, called the domain of the map; a set $B$, called the codomain of the map; a rule assigning to each element ...
4
votes
5answers
4k views

Graph Theory Applications?

What are the areas where graph theory can be applied? Cause I wonder what applications this have on the real world. Does it solve certain problems and stuff? Areas such as communication networks ...
4
votes
2answers
90 views

Expository problems

In one article on his blog; T. Gowers talks about ''expository problems''. For those too lazy to click that link, a quote of a quote: Solving an open exposition problem means explaining a ...
1
vote
2answers
113 views

Types of numbers.

Is there a comprehensive list of real-number-describers that allude to the properties of that number? For example: Amicable numbers, Abundant, Deficient, Perfect, Carmichael, prime, transcendental, ...
9
votes
1answer
291 views

What would happen if we created a vector space over an integral domain/ring.

I've always been curious about this, why do we use fields as the only algebraic structure to put vector spaces over? It seems a bit arbitrary to me, so I was wondering what would happen it we replaced ...
6
votes
1answer
341 views

Age of Stochasticity?

Today I came across D. Mumford's 1999 article The Dawning of the Age of Stochasticity, which is quite remarkable even after more than a decade. The title already indicates the theme, but I copy the ...
3
votes
4answers
76 views

Unable To Understand The Difference Between $(-3)^4$ And $-3^4$

Why is $(-3)^4 =81$ and $-3^4 =-81 $?This might be the most stupidest question that you might have encountered,but unfortunately i'am unable to understand this.
21
votes
8answers
35k views

“Where” exactly are complex numbers used “in the real world”?

I've always enjoyed solving problems in the complex world during my undergrad. However, I've always wondered where are they used and for what? In my domain (computer science) I've rarely seen it be ...
2
votes
5answers
719 views

What's the importance of “infinitesimally small” whenever calculus is explained

First of all, i just like reading and understanding things related to math, but NOT at all any expert in math. So, I apologize if the question seems dumb. It always puzzles me whenever a basic ...
19
votes
2answers
6k views

Path to Basics in Algebraic Geometry from HS Algebra and Calculus?

In this question, Why study Algebraic Geometry?, Javier Álvarez, develops a succint but encompassing description of algebraic geometry and its spread across different areas of mathematics. Indeed, it ...
9
votes
8answers
780 views

“How I wish I could calculate pi” analogs…

You might know the mnemonic for $\pi$ in the title or even this more elaborated one: Sir, I bear a rhyme excelling In mystic force, and magic spelling Celestial sprites elucidate All my own ...
26
votes
6answers
2k views

How to read letters such as $\mathbb A$, $\mathbb B$, etc., or $\mathfrak A$, $\mathfrak B$, etc.?

This is a soft question. We can read the letters $\bf A$, $\bf B$, etc. as bold A, bold B, etc. We can read the letters $\textit{A}$, $\textit{B}$, etc. as italic A, italic B, etc. We can read the ...
13
votes
1answer
450 views

Developing research experience in mathematics

I am not sure whether this is the right forum for this question, so it might be migrated somewhere else; but, it is, I think, certainly germane to the wider idea of pursuing interesting questions and ...
15
votes
3answers
2k 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 ...
5
votes
4answers
4k 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
2
votes
1answer
124 views

Finding his own path [closed]

I am a graduate student in major mathematics and now the time has come to choose a "specialization" (I have to choose 3 between 4 subjects). I like algebra a lot and I am also interested in ...
4
votes
3answers
235 views

Theory of Equations and Undergraduate Mathematics

I was browsing through a book entitled: Field Theory and Its Classical Problems by Charles Hadlock, one of the Carus Mathematical Monographs titles. In his preface he says the following: In ...