# Tagged Questions

The process of studying mathematics without formal instruction. _Don't_ use this tag just because you were self-studying when you came across the mathematical question you're asking; it is only for when the fact that you're self-studying is what your question is _about_.

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### Why learning modern algebraic geometry is so complicated?

Many students - myself included - have a lot of problems in learning scheme theory. I don't think that the obstacle is the extreme abstraction of the subject, on the contrary, this is really the ...
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### Min problem by using Lagrange method

$$\min x^2+y^2$$ $$\text{s.t.}\ \ (x-2)^2+(y-3)^2\le 4 \ \ \ \text{and} \ \ \ x^2=4y$$ Please explicitly solve this question by using Lagrange multiplier method. I accept $(x-2)^2+(y-3)^2=4$ ...
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### Drawing 2D plot of xy

I need to graph the plot the intersection of xy and $x^2+y^2=1$ We know that $x^2+y^2=1$ is a unit circle. And by using wolfaplha website, I get the following 3D plot of xy ...
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### Self Learner learning Calculus, Linear Algebra and Discrete Mathematics [on hold]

I am learning Algebra 2 and Pre-Calculus on Khan Academy in preparation of learning higher mathematics such as Calculus, Linear Algebra and Discrete Mathematics. There are interactive courses such as ...
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### Maximization problem on an ellipsoid [on hold]

for three variables, $$\max f(x,y,z)= xyz \\ \text{s.t.} \ \ (\frac{x}{a})^2+(\frac{y}{b})^2+(\frac{z}{c})^2=1$$ where $a,b,c$ are constant how to solve the maximization optimization problem? ...
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### How to write a discrete dynamical system into first order system

I need guidance on how to solve this here. $$x_{n+1} + 3x_n - 4x_{n-1} = (\sqrt{2})^n cos \left(\frac{n\pi}{6}\right)$$ I am required to transform the above equation into a first order finite ...
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### When to do exercises?

Let's assume I'm reading a book on stochastic calculus. Usually, I do it in 3 passes: Pass 1: Skip proofs, just read definitions, lemmas and theorems. Think about assumptions and why they are ...
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### Offline resources for serious students of mathematics in the San Francisco Bay Area [closed]

What local resources exist for the serious student of mathematics residing in the San Francisco Bay Area? By "serious student", I mean someone of any age and academic status devoting substantial ...
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### Learning to understand proofs faster?

There are many books, written by highly decorated academics, which feature proofs that I can hardly comprehend in an acceptable amount of time. Roughly each week, it happens that I find myself having ...
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### How can we prove $e^{\pi}-\pi\simeq 20$ geometrically? [closed]

Using a calculator we can easily check that $$\color{Green}{e^{\pi}-\pi}=19.999\cdots\color{Green}{\approx 20}$$ This article and this one provides some details about this almost near identity, but no ...
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### Confusing about coordinate curves and quadrilateral formed?

Below is a problem which states a fact about "Tchebyshef net". I don't understand meaning of bolded part. The coordinate curves of a parametrization $x(u, v)$ constitute a Tchebyshef net if the ...
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### Marginalizing multivariate-normal distribution canonical form

Regarding the problem of margenalization of canonical forms of multivariate gaussian distribution it was mentioned in probabilistic graphical models text book that $$\int{C(X,Y;k,h,g)}dY$$ is ...
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### A path to more advanced math topics.

I am from Hong Kong and have just finished all the public exams. In my high school life, I've learned some topics on mathematics which are fundamental, yet I think are not in-depth enough. The topics ...
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### Expectation Functional in Lebesgue and Riemann Terms – Looking for a clarification

Here there is a really central problem I am having self-studying probability theory, that concerns the relation between the definition of expectation in Lebesgue terms and in Riemann terms. I will ...
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### Vladimir Zorich vs Rudin/Pugh/Abbott

There have been various comparisons between books on Analysis. I was surprised to find out that Zorich's book on Analysis was not compared anywhere. Can anyone give a comparison between Zorich and ...
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### Negative Mean Square Error

For simple random sampling, I have calculated somemean square errors for ratio-type estimators such as Isaki estimator, and Prasad Singh estimator. But, Mean Square Errors i obtained are negative. ...
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### Is It Worth It Working Out Every Practice Problem In Math? (Without a calculator)

I'm bouncing back between trig, algebra, and calc books. I've noticed that most of the problems at some point seem to distill into very tedious arithmetic. It is nice to have the prowess of ...
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### Equivalent systems of Linear equation

I've just begun to re-learn linear algebra because is so important, the book that I chose is naturally the Hoffman's for a lot of reason. Well, In the first chapter I'm stuck with the following, ...
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### Suitable reference for learning symplectic geometry

I am interested in studying symplectic geometry by myself and I'm looking for a good text to use as a reference in the way. I am a bit lost because I've found a lot of notes and books on the subject ...
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### Question about the mathematics in actuarial studies

I tried Google but there isn't much information on this and I would really like some insights into actuarial studies, the mathematics involved and how it compars to the mathematics in a bachelor of ...
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### writing a piecewise regression model as a linear model

lets write the following piecewise regression model $$y= \alpha_0 + \alpha_1 x +\epsilon ;\ \ x\le x_0$$ $$y=\beta_0 +\beta_1 x + \epsilon \ \ x\gt x_0$$ according to the variable $x_0$ is ...
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### Does the phrase “If you don't use it, you lose it” apply to mathematics? [closed]

I'm asking this because I ran into the following particular situation: I took some calc courses over 2013, where I learned, amongst other things, to integrate some pretty nasty functions, and this ...
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### Bolzano-Weierstrass Theorem proof question

Since $[a_n,b_n] \subset [x,y] \forall n$, we know that $Q = \{a_n\}^\infty_{n=1}$is bounded Let $t= \sup Q$ (which will be the accumulation point) Let $P$ be any neighborhood of $t$, so that there ...
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### Most efficient way to learn mathematics

So there's a lot of advice on how to learn mathematics most efficiently, and it mostly revolves around doing problems, asking questions, and considering all possible generalizations. However, I was ...
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### What is the proper way to study (more advanced) math?

Here's what happens. I get stuck on some proof or some mathematical construction and I end up staring at the problem for hours, sometimes not making any progress. I do this because sometimes I think ...
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### Self learning complex systems modeling

I am currently a senior studying mathematics. My program is heavily focused on pure maths, however, my interests lie in the area of applied mathematics. Specifically, I am interested in the study of ...
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### Between Oksendal and Karatzas books

I finished Oksendal "SDE , an introduction with applications" , did most of the exercises (not all with success, but I read the solutions for those); my next project would be to read the Karatzas ...
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### Self-teaching myself math from pre-calc and beyond.

Going to be starting grade 12 (pre-calculus) shortly and looking to get ahead. I would like to try some more rigorous stuff on my own and have a couple questions. Ideally I would like to be prepared ...
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### Why is cross product only defined in 3 and 7 dimensions? [duplicate]

Why $3$ and $7$? I know from some reading that Hurwitz's Theorem explains this, but can someone help me build some intuition behind this or perhaps provide a simpler explanation? It still seems ...
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### Is there any closed form for the finite sum $1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+…+\dfrac{1}{n}?$ [duplicate]

I know that the infinite summation $$1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{n}+...$$ is divergent and also the sequence 1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{n}-\ln ...
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