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Questions tagged [learning]

Questions about the process of learning mathematics, both inside and outside a formal environment, including learning strategies, recommendations for learning particular subjects, and studying habits.

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3answers
49 views

Good way of learning math

In my secondary school, I have been copying the solutions of the questions I could not solve and I guess this helps you to memorize (not blind memorization, sending the info to long term memory). Do ...
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1answer
9 views

Compute the conditional expectation when brownian motion is involved

Consider the following conditional expectation $E[(x_t + \mu(s-t) + \sigma(\beta_s - \beta_t) )^2 | F_t] $ where $\beta_s$ and $\beta_t$ are brownian motion. Then, = $E[x^2_t + 2x_t\mu(s-t) + ...
2
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0answers
57 views

No Free Lunch in statistics

I was wondering if the No Free Lunch (NFL) theorem applies to even the estimation problem. Suppose there are $N$ points in the input. We are trying to estimate the mean value say weights associated ...
1
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0answers
35 views

How to approach a new subject? [closed]

In William Thurston's Essay On Proof and Progress in Mathematics, he states that what mathematicians want most is an understanding of mathematics. This got me thinking, how do you all approach a new ...
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2answers
44 views

How to determine the correct integrals

Suppose you are given the following joint probability distribution $ f(x,z) = (8x^2z + z^2) \text{ where } 1 \leq x \leq 2, 1 \leq z \leq 2 $ and you what to find $P(X + Z > 2.5)$. How do you ...
3
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1answer
113 views

(Soft question) How to study for a proof-based math class?

I'm an undergrad at a top US university and I'm currently taking an Introduction to Analysis class. I really really enjoy this class and it's actually getting me more interested in math in general. I ...
5
votes
1answer
132 views

(Soft question) Should you struggle with every question in the textbook or look at the solution manual for some?

I'm currently in a class that uses Spivak's Calculus. Because of (fairly) good explanations and proofs, fun and challenging exercises, and some witty comments he gives occasionally, I really enjoy ...
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0answers
36 views

Was my skepsis justified?

The other day I got asked to answer a survey, in order to get to know, why people sometimes have problems learning limits. I got asked some, in my humble opinion, rather easy questions for a math ...
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1answer
43 views

Combinatorics, number theory, and graph theory, in what order should they be learnt?

Combinatorics, number theory, and graph theory, in what order should they be learnt? I would like to learn discrete math; these are the three main branches that compose it. I was wondering if there's ...
0
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0answers
39 views

If any alternative numbering systems exist that simplify thinking about arbitrary numbers [duplicate]

In modern Western culture we think of numbers typically in base 10. By "we" I mean the vast majority of the public. For some reason this is easy, and I'm not sure why or how to pinpoint it down to ...
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0answers
72 views

Long derivative exercises: where to find them?

I am preparing for an exam. On the exam I will be asked to find the derivative of a long function, with a multiple chain rule. Such as: $$y = (\frac{3}{x} - 2^{{x}^3})^{6} + \frac{\ln \sin \frac{2x+1}{...
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0answers
44 views

Measure of Improvement in Math Skills from Remediation with ALEKS

I am analyzing some data on ALEKS for my home institution. Specifically, I am analyzing placement scores for ALEKS where the students are allowed to take the placement test multiple times and are ...
0
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1answer
84 views

What is the best way to learn mathematics? [closed]

As the title, I concern about what is the best way to learn mathematics. I've asked some of the professors in my university. Some said that I should intuitively understand mathematical concepts and ...
1
vote
1answer
36 views

How to make a kid understand geometry and help him solve problems?

I'm tutoring a 13 year-old boy, a middle school student. He has almost no problem with elementary algebra: he just applies the rules and everything falls into place. However he does struggle with ...
5
votes
1answer
133 views

Who said (a variation of) this? “Mathematics didn't teach me how to reason correctly, but […] how easy it is to make an error when reasoning.”

I remember I once read a quote of a mathematician at the beginning of a book, or article, which said a (possibly) small variation of: Mathematics didn't teach me how to reason correctly, but at ...
2
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1answer
75 views

Being less sloppy while doing exercises

I'm working through a pre-calculus course and I'm getting bad results while reviewing my exercises with the answers. It's not that I don't grasp the concepts, I make notes of the concepts, with ...
1
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1answer
58 views

Find a vector that will make the set linearly independent

I have a set of vectors in $\mathbb{R}^{3}$: $\Biggl{\{}$$\begin{bmatrix}1\\2\\3\end{bmatrix}$,$\begin{bmatrix}-2\\2\\-3\end{bmatrix}$,$\mathbf{\vec{v}}$$\Biggl{\}}$ I want to be able to find the ...
3
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1answer
209 views

What Field(s) Cover Calculus with Matrices and High Dimensional Geometry?

I am taking a course in machine learning and have found that the linear algebra and multivariable calculus from my engineering degree only take me part way in understanding some derivations. One ...
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1answer
70 views

I want to learn more mathematics [closed]

I'm a computer science student, but I'm not satisfied with my math skills. I need suggestions on how to improve my math skills, including books for beginners and the like.
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0answers
18 views

How are the values found for the bias and variance of kNN from this website example?

At the website http://scott.fortmann-roe.com/docs/BiasVariance.html, in section 3.3, an explicit analytical expression is given for the bias variance trade off equation. Can someone please explain how ...
3
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0answers
58 views

Math Major Having Trouble [closed]

I am a freshman at Alfred University. I've been out of school for 6 years and am returning as a non-traditional student. I'm having some trouble that I hope someone may have insight for me. I love ...
3
votes
1answer
127 views

Good Proof Problems for a High School Student?

High school student here... So recently, I have accomplished what I am considering the most exciting breakthrough of my mathematical journey so far... I WROTE A PROOF! I proved that the sum of any ...
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0answers
53 views

Soft Question: How to adapt to different Mathematical models and proper counting practices

I am an undergraduate studying Computer Science, and currently doing some advanced programming modules, hardware modules which work with binary arithmetic, some mathematical modules which might be ...
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2answers
1k views

Do Math Professors still do textbook problems to learn subjects foreign to them? [closed]

This question is very subjective and is of no technical detail, however since MSE is a place for working mathematicians, I thought I'd ask here to get the best answers! As a prospective graduate ...
2
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0answers
68 views

What is the meaning of subsampling level in machine learning/statistics?

I am reading a paper but nowhere it is defined but the term is being used a lot. The paper is - Less is More : Nystrom Computational Regularization -Rudi,Camariano, Rosasco Link : ...
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2answers
143 views

Learning math while visually impaired

My eyes are destroyed. I have been unable to learn math beyond decimal division in school due to laziness and unhelpful teachers. I am now trying to mitigate this mistake by learning math from the ...
5
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5answers
212 views

Is there a flowchart with a DAG of the different branches of mathematics?

I'd like to dip my toes into some specific areas of mathematics (like Category Theory) and my problem is that I did not find a flow chart which displays how different branches of mathematics depend on ...
3
votes
1answer
113 views

How to get a sense of big picture/explore and find stuff while learning math

Someone who is really good at math (and did algebraic geometry in high school, 3x Putnam Fellow, 2x IMO Gold and currently doing world-class research in algebraic geometry) wrote (while he was still ...
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1answer
107 views

Having trouble gaining mathematical intuition

I recently started studying advanced mathematics on my own, after taking two classes in college (discrete math and advanced mathematical logic) that spurred my interest in the topic. However, I am ...
5
votes
3answers
179 views

proper way to approach learning higher (university level) mathematics

I have been struggling to self-learn some somewhat higher mathematics- mostly university level mathematics. However, I've looked up other questions and they didn't mostly line up with what I am ...
2
votes
2answers
64 views

Learning approach and book reccomendations for having had little to no math in school.

I am 22 years old and I am looking to develop my understanding and knowledge in math to be ready for Computer science related courses. I am currently working as a software engineer (self taught). But ...
0
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0answers
53 views

Soft question: What are some good calculus resources

I am a high school junior searching for decent calculus texts to strengthen my grasp on the subject. I am going advanced than my school course and am currently learning multi-variable calculus from ...
0
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1answer
19 views

Point of intersection in two-variable equation

I am trying to solve seemingly a very simple set of equations. Following two equations are the success probability for the transmit powers $P_m, P_u$. $$x_1 = \frac{1}{1 + ab\frac{P_u}{P_m}}$$ $$x_2 ...
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1answer
56 views

is it possible to visualize every math problem in the world? [closed]

It is the era that is called internet era,people are more connected today everything is being simplified extremely. We all believe that visual learning is more stronger than merely reading or ...
1
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1answer
76 views

Physics and Differential Geometry

Currently I have asked to me if physics is needed to study differential geometry. I know that in the theory, we can study differential geometry without any concept of physics; however, so many ideas ...
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2answers
33 views

Rules for multiplication serge lange problem

I have recently started to get interested in math for self learning and recently acquired Serge Langs "Basic Mathematics" I found myself stuck, trying to figure out one of his proofs regarding more ...
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0answers
109 views

Different true/false definition in lambda calculus

How to deal with different definition true/false. In standard conception is true defined as taking the first value and false as taking the second one. Let's say we have true/false defined as follows: ...
3
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1answer
79 views

How do/did you go about learning math? [closed]

I have wanted to improve in math, so I could do computer science, and generally develop math skills. However, the process has been chunky. I can summarize it into these three issues: Understanding, ...
1
vote
4answers
311 views

Using Visualization for Learning: $a^0=1$ [closed]

Honestly, this was a question from a student. I show $\forall a\in \mathbb{R}-\{0\}:a^0=1$ for the class. $$1=\frac{a^m}{a^m}=a^{m-m}=a^0$$or $$a^{m}=a^{m+0}\to a^m=a^m\times a^0\\(a\neq 0) \to cancel ...
3
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3answers
171 views

Worrying about logic and foundations too much [closed]

I am studying undergraduate physics and I am always interested in why we consider certain physical models instead of the others. That ultimately leads to the question why we consider one mathematical ...
0
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1answer
60 views

Beggining in funcional analysis [duplicate]

I get bogged down with notation as well as its mechanics and am in need of a textbook. What are good begginer's textbooks for functional analysis? Thanks.
0
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1answer
124 views

If you had to self -study a course in higher math that you know, and passing it was a matter of life and death, what advice would you give yourself?

How would you relearn a course at a level where you could pass a university exam but you had to self-study? To set the scene: If your memory of a higher level math subject (like the real analysis) ...
2
votes
1answer
193 views

Can the action-value function be “expanded”?

I know the basic language of probability, but not fluent in it, and the text books on reinforcement learning usually assumes one is fluent in it, so they don't define everything rigorously, here is my ...
2
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3answers
224 views

Is it good to learn measure theory before topology or the other way around?

What would be the best way to go about learning topology and measure theory? Does topology make analysis easier to understand? Or does learning measure theory beforehand make topology easier to ...
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1answer
589 views

What is the determinant modulo 2?

I was looking at an old post and want to learn about why the answer is true. I have taken linear algebra but never heard about this. Where can I learn this?
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0answers
138 views

How far in topics does Spivak's Calculus cover?

For example, would it go all the way to Differential Equations? I want to get my money's worth. I want to learn up to Differential Equations for now, but I want a rigorous proof based style even ...
0
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1answer
624 views

Converting a Linear Programming problem for solving using Machine Learning

I have a typical linear programming optimization problem with a huge data set (millions of records and upwards of 150 GB data file). The size of the data is causing cost issues for reaching an optimal ...
4
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1answer
120 views

Studying ODEs… is it worth it?

I am a first year Master's student in applied mathematics. I'm currently taking a Mathematical Physics class and we have been studying techniques for solving ODEs. There is some overlap with undergrad ...
2
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1answer
62 views

Root/Solution confusion

Suppose I have the equation $x-a=0$. So, $x-a=0\Rightarrow x=a$. The unique solution is (or root) $a$ (by definition a solution is the value for the unknown that make the equation true, $a-a=0$ ). ...
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4answers
320 views

When learning mathematics should one prove everything one learns?

I sat through a real analysis class around a year ago and in about two days we partially covered the construction of the real numbers as equivalence classes of Cauchy sequences. Through the teacher ...