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4 views

Prequisites for chemical reaction network theory

What are the prequisites for chemical reaction network theory? Furthermore, can anyone please suggest some introductory material into the field. I thank you in advance.
6
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0answers
47 views

Imaginary Number in Logic

The equation $x^2 = -1$ was once said to have no solution. Then the number $i$ was discovered (or invented?) and our number system got richer. In particular, in this new wonderful world of complex ...
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0answers
18 views

Is there any solution manual to Halmos' Measure Theory?

I've spent some time on Halmos' Measure Theory and must upvote such a good book. I want to solve most exercises in this book. I'm not sure whether there is a solution manual or instructor manual that ...
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2answers
19 views

Volume question

A box holds small cube shaped blocks that are the same size. Kim tires tk build a large cube out of the small blocks but finds that she needs 6 more blocks. Takashi builds a different sized cube out ...
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0answers
19 views

Examples of Lp spaces in Applied Math

I was wondering if there are examples of exotic Lp spaces being used in applied mathematics. I know that the "special" p's (1,2 , infinity ) are of use, for example in statistics, L1 is mean, L2 is ...
15
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2answers
1k views

Who is the “father of number theory”?

I noticed that some sources state Fermat as the father of modern number theory while others say Gauss. I am trying to start a paper on the history of number theory for a presentation, but I cannot ...
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2answers
52 views

Fermat's Last Theorem - Variation with arithmetically descending exponents

Are there solution(s) to the following variant of Fermat's Last Theorem in the positive integers? $$ a^n + b^{n-i} = c^{n-2i} $$ I haven't been able to identify any trivial solutions. To my ...
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1answer
27 views

Notation methods for the following things? [on hold]

I go to a high school that rushes concept and does not ever talk about notation. I want to be prepared for college, and not be swamped by all this notation I don't know. From SE, I would like to know ...
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5answers
3k views

Opposite of Fermat's Last Theorem?

So Wiles' proof showed that no three positive integers $a$, $b$, and $c$ can solve the equation $a^n+b^n=c^n$ for any integer value of n greater than $2$. Now what about the opposite? What does this ...
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0answers
31 views

Is embedding a function make sense?

The embedding is defined in the wikipedia link as "In mathematics, an embedding (or imbedding [1]) is one instance of some mathematical structure contained within another instance, such as a group ...
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0answers
25 views

On classification of directed topological spaces [on hold]

Is classification of directed topological spaces (not their homotopy equivalence classes!) an important subject in modern mathematics?
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0answers
99 views

Do “my” notations already exist or not?

Because I'm a bit slow to write my lessons, when I was in classroom, especially in maths, I created my notations as the same way as notations normaly used. For example in maths we prefer write ...
2
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0answers
20 views

List of textbooks that take a historical approach

As the title suggests my aim in this topic is to make a big list of textbooks on any mathematical topic that take a historical approach. I will start with the ones I know: Thomas Muir - The theory of ...
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0answers
26 views

Abbreviating the definition of a tangent vector field?

Let $A \subset \mathbb{R}^{n}$ be open in $\mathbb{R}^{n}$ and let $F: A \to \mathbb{R}^{n} \times \mathbb{R}^{n}$ be continuous. Then $F$ is called a tangent vector field on $A$ if and only if $F(x) ...
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1answer
24 views

Notation and name for this function?

Let $k \geq 1$; let $V,W$ be vector spaces; and let $T: V \to W$ be linear. Then how do we call and denote the function $(v_{1},\cdots, v_{k}) \mapsto (T(v_{1}), \cdots, T(v_{k})): V^{k} \to W^{k}$?
2
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1answer
14 views

Definition of linear independence in R-module

I am revising module theory over commutative rings with 1 and I have a "soft" question regarding to why don't we define linear independence as follows: "$v_1,...,v_n$ are linearly independent if ...
0
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0answers
11 views

Number of possible non crossing paths on a grid of $m$ by $n$ size?

Given two points on 2 dimensional m by n grid, moving in units of 1 in either direction, how many non intersecting paths exist between the two points? in other words, with taxi cab metric, on a m by ...
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2answers
82 views

What is the most complex mathematical topic? [on hold]

I'm a simple man living my simple life and often I like to learn more about math and science. Today my daughter asked me about how many numbers are there and I explained that there are infinite ...
3
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1answer
51 views

The sections of the projection $\bigsqcup_{i:I} X_i \rightarrow I.$

I just noticed something funky. Let $X$ denote an $I$-indexed family of sets. There is a projection $$\pi_X: \bigsqcup_{i:I} X_i \rightarrow I.$$ It isn't necessarily surjective, of course, because ...
2
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0answers
14 views

What is the purpose of continuous and differentiable dependence

In learning Gronwall's inequality you also get to learn about continuous an differentiable dependence. I know the theorems but I have no idea about their application. What is the big idea of ...
7
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1answer
145 views

What did Lagrange, Euler, Gauss etc. learn in order to know what they knew?

What did the great mathematician, like Cauchy, Lagrange, Euler and Gauss, learn in order to know what they knew? It seems that they were extremely good in the most basic rules/structures/issues of ...
0
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0answers
33 views

Is math, in the end, only geometry [on hold]

When thinking about the Universe, or "reality", Isn't every part of mathematics a tool for expressing something geometrically further down the line? Yes, every part of math is related, but isn't ...
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0answers
26 views

How important is it that I study Probability if I like Analysis/Algebra much more?

Is it crucial to a student's undergraduate studies in Math that he/she takes a course in Probability and/or Statistics? I am much more interested in Analysis/ Algebra and I was wondering if it would ...
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0answers
16 views

Can we build a DFA less than 5 state for word length 4( 1100)? [on hold]

========================================================== 1 if possible kindly, help me with this question.
3
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1answer
61 views

What solution would you come up with for this problem?

So the question is: put numbers $1, 3, 5, 7, 9, 11, 13$ and $15$ into gaps in the following expression: $$\_\_ + \_\_ + \_\_ = 30$$ The most naive approach to use summation in the group of integers ...
1
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4answers
62 views

Why in general there is no systematic way to find counterexamples? What kind of property do they all break that lead to this? and other things

We came across counterexamples in many areas of mathematics: For example Sum of irrational numbers not necessary being irrational The "Windmill blade" function (for lack of a better name of one of ...
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2answers
29 views

Encyclopedia of Mathematics?(non-Alphabetical)

Do you know any Encyclopedia of Mathematics which is in non-alphabetical order, like it starts from basic mathematics and then goes up to very advanced level. And what's the difference between say, ...
3
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2answers
228 views

Can I follow a graduate course in PDE without having studied ODE

Hi I am considering taking the first course on Partial differential equations at my university next semester. I have already taken a first course on functional analysis . I haven't taken a proof based ...
1
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0answers
57 views

How to invent mathematics to find solution to real world problems?(without high level mathematical knowledge) [on hold]

Let's say I want to know how waves are formed when a stone is dropped in water, how trees are deformed by the wind, etc, and I want to invent the mathematical equation to predict the behaviour of ...
1
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1answer
31 views

How do we call a pair of sets $A,B$ such that there is some injection $f: A \to B$?

Let $A,B$ be sets and let $f: A \to B$. If $f$ is a surjection, then we may simply write $f(A) = B$ or say in a more laborious way that $f$ maps $A$ onto $B$, to mean the same thing. However, if $f$ ...
4
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2answers
221 views

How do we call a pair of sets between which there is a bijection that need not have additional property?

Let $A,B$ be sets and let $f: A \to B$. Then we say that $A,B$ are isomorphic under $f$ if $f$ is a linear function that maps $A$ onto $B$ in a one-to-one manner; that $A,B$ are homeomorphic under $f$ ...
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0answers
90 views

Mathematicians who didn't study mathematics in college or university [closed]

I would like to know mathematicians born after 1900 who didn't study mathematics in college or university. I posted a similar question recently but it was closed as opinion based. So I will define ...
7
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3answers
160 views

A reason for the value of $\int_{0}^{1}\log{(x)}\log{(1-x)}\,\mathrm{d}x$

In this .pdf document, which is just a list of Putnam-style undergraduate-level problems from various sources, the third question is as I have stated it below (up to a change of notation). ...
1
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3answers
97 views

Good algebra book to cover these topics?

I will be studying two algebra modules next year and I am looking for a comprehensive book that will cover both of them, however due to having very minmal exprience with algebra I am looking for your ...
0
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3answers
84 views

How would you explain Functional Integration to an 8 year old?

I get the definition of the Functional Integral, but what heuristic interpretations are available to better understand the integral? For instance, what motivates the definition? How is it related to ...
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1answer
43 views

What are some easier papers/books I can read? [closed]

I'm trying to improve my ability in reading mathematics papers. My field is more related to biological sciences, but there are a lot of interesting papers I'd like to read that use more mathematical ...
5
votes
1answer
42 views

Does it matter if you use big $L$ or little $l$ when talking about $L$-norms?

I was reading a post on Quora regarding the application of "$l_1$", "$l_2$" norms for convex linear programming when I became very confused at which $L$-norm the posters are actually referring to. I ...
2
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3answers
93 views

Fun logic puzzles to teach logic/proof-writing to students

Forgive me if this is too soft of a question, but I am looking for some fun, quick, and interesting logic puzzles to give to my students. I'm teaching an honors calculus course, and this will be their ...
2
votes
1answer
63 views

Intuition for Burnside's Lemma (aka Cauchy-Frobenius Lemma)

Here is the theorem: Lemma: Let a group $G$ act on a set $S$. Define $\text{Fix}(g)$ as the set of all elements in $S$ fixed by $g$ under this group action. Then the number of distinct orbits of ...
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0answers
32 views

In what ways would a course on convex optimization be useful in game theory?

From talking to several other people in the past, and referencing Quora, it seems that convex optimization is really a tiny subset of game theory in that it only models the behavior of one single ...
2
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3answers
75 views

How do mathematician make sense of “outcome” and “events” in probability?

One of the biggest challenge for me to understand probability is to make sense of this concept of outcomes and events. To put it plainly, it just doesn't feel like mathematics anymore when we talk ...
5
votes
1answer
48 views

Stating the induction hypothesis

I would like to ask about the best way to state the induction hypothesis in a proof by induction. Just to use a concrete example, suppose I wanted to prove that $n!\ge 2^{n-1}$ for every positive ...
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1answer
16 views

Zeitz's ACoPS vs Larson's PSTP

Which of the following books is better to prepare for a mathematical competition at the undergraduate level? The art and craft of problem solving (ACoPS) or Problem solving through problems (PSTP). ...
1
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2answers
43 views

How to document solutions for future use? [closed]

I'm taking courses of math at university level, it's kind of the equivalent of master degree in mathematics, I'm from Argentina. The way to learn mth in my university is this: We attend lectures, we ...
1
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0answers
34 views

Is there anything called kernel space?

Here I am referring kernel as an integral operation.The wikipedia link is this https://en.wikipedia.org/wiki/Integral_transform My question is: consider the function insider the integral $f(t)$ is ...
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0answers
56 views

Magic of the number $2000+15$ [closed]

What is the most clever way of getting the number $2015$ using only addition, subtraction, and multiplication?
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3answers
69 views

Motivations for Hyperbolic Geometry

Why would one study hyperbolic geometry? I am only aware of the motivation where you give axioms for elementary euclidean geometry and then start to wonder wether the parallel axiom is necessary. You ...
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1answer
78 views

Struggling to stay at current course.

Disclaimer: I'd like to say I've been a member of this site for over a year, so I know this may be a nonstandard question, however, for personal reasons, I'd like to keep this anonymous. I'm a second ...
1
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3answers
66 views

Acronyms and words as variables and in mathematical notation

I am unsure if this question is warranted. Often mathematical symbols and objects are represented by a single character, e.g. variables are most often single characters like $x$, and often to ...
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0answers
24 views

About Carl Meyer's matrix analysis

I have taught some part of it to myself when i was an engineering student. but now i changed my major to the pure math so now i am studying math as an undergraduate student. i thought the book is ...