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1answer
152 views

Learning roadmap for additive combinatorics

I have read Calculus by Michael Spivak. Now I want to learn additive combinatorics though I have no experience with combinatorics or probability theory. To my understanding, there is a book on the ...
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1answer
56 views

Recursive application of a function : Symbol of [duplicate]

I need to apply a function $f(x)$ recursively/repeatedly for n times; how do I express it (mathematically) ? Is their a mathematical symbol which denotes $f(x)$ applied n times ie $g(x,n)$ ...
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1answer
1k 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 ...
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2answers
1k views

Book Reference for Calculus and Linear Algebra :: Engineer

I'm almost through with my (Mech.) engineering and am trying to touch some advanced concepts in Computational Science which requires me to study Calculus and Linear Algebra in a more theoretical ...
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1answer
166 views

What is an honest basis?

In a comment to this question, the commentator stated that "the monomials form an honest basis for your vector space". To be honest, I never heard of that. Is this something elementary?
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1answer
361 views

What does “a set of things” mean?

Suppose we defined some mathematical object $P$, where $P$ is natural number, polynomial, endofunction, geometric figure, etc. What does the expression “$A$ is a set of $P$s” mean: Set inclusion) ...
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0answers
30 views

Uniform distribution on convex hull

Let $X=\{ x_1,\dots,x_n \} \subset \mathbb{R}^m$. Let $H(X)$ be the convex hull of $X$. Assume that $X$ is a convexly independent set, i.e. none of the $x_i$ are a convex combination of the others. ...
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1answer
51 views

Writing a chain of implications in English

How to write a theorem of the form $A\Rightarrow B\Rightarrow C\Rightarrow D$ where every $A$, $B$, $C$, $D$ are formulated with words (English) rather than with formulas? One idea: The next item of ...
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0answers
37 views

Intuition analysis-deconstruction-reconstruction.

The following question is a refinement of this question, which caused a lot of people to give answers that were missing the point entirely, probably because the question was not clear. Being human, ...
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1answer
107 views

Books (and supporting material) that are useful in deconstructing one's intuition?

I recently came across the following problem from Paul Zeitz's book The Art and Craft of Problem Solving. Given the image below, can you find a way to connect corresponding blocks (i.e. A to A, B to ...
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1answer
244 views

Formula to calculate difference between two dates

I am working on getting date difference I have a formula to calculate it as follows $$365\cdot\mathrm{year} + \frac{\mathrm{year}}4 - \frac{\mathrm{year}}{100} + \frac{\mathrm{year}}{400} + ...
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2answers
107 views

Why do we use “if” in the definitions instead of “if and only if”? [duplicate]

I often write my notes as logical statements and constantly wonder why people use only the "if" direction in the definitions instead of the "if and only if". Consider: "A homomorphism $\phi$ is said ...
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49 views

Mapping Normal distribution to a new bounded distribution.

My question is vague. I am looking for distributions that can be obtained from Normal distribution by mapping it to a bounded interval. "By mapping" I mean that a probability distribution ...
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1answer
270 views

What are the prerequisite for understanding complex analysis?

Which should I complete first before complex analysis? I am following Visual Complex Analysis by Tristan Needham. Is there any easier book?
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1answer
135 views

What does it mean for a random variable to describe an experiment?

I often hear the expression, random variable (or sequence of rd's) to describes an experiment (or sequence of experiments. But that sound totally unrigorous to me: So we're given a mapping $X:\Omega ...
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2answers
2k views

What are the cutting-edge topics in modern math? [closed]

What are the latest major discoveries in math? What areas and problems are considered important for overall advance of math? Also, given that most of those topics are most likely very advanced - what ...