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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How do I improve my mathematical skills/techniques?
When I mention skills and techniques, I mean the complete range of problem-solving tools, including tricks, and an innate sense of calculation. I'm quite adept at using category theory as a learning ...
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need help with majoring in engineering technology
I am 32 years old. I'm majoring in engineering technology, but I still have problems with advanced calculations, such as calculations of material resistance. I would like to improve my math and ...
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How to take maths notes, and generally to work with them, in order to understand as much as you can as best as you can?
I have hit a bit of a roadblock in my undergraduate studies. Our lectures assume that we should be taking notes, and that is entirely understandable: after all, what else can you be doing during a ...
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Compilation of Phenomena Modeled by an Operation Table
It seems like there would be utility in a search engine or database through which the user inputs the operation table of a magma (I think that's the right level of algebraic structural generality) to ...
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How do mathematicians keep track of thoughts in a quick and reproducible manner [closed]
The way I work on homework questions, especially for analysis and topology, might be a little different (or maybe not). I would remember the questions and think of them when I run, take a shower, and ...
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Does practicing mental math increase mathematical intuition? [closed]
Has any experienced mathematician on this site found that practicing mental math was associated with the development of mathematical intuition and conceptual understanding? I was considering ...
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How can I improve my comprehension of mathematical notation and avoid getting lost in the details, when there's no obvious visualization to rely on?
For context, I'm an engineering student nearing the end of my degree and I've been tutoring algebra, calculus, and statistics for years, so I'm not a newbie to math. It's only really been an issue in ...
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I dont understand this problem [closed]
How is the answer to this not -6? Please solve this without U substitution because I need to know what I did wrong to get a negative answer. I did interval (B) - (A) as you should
$$\int_{-21}^0 \...
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Methodology for solving graduate mathematics problems
Recently, I have been introduced to graduate mathematics, and I am doing graduate courses, in these courses we have homework and the problems tend to be challenging.
In comparison to undergraduate ...
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Example of tightness of Sauer-Shelah lemma
I was given the task of finding an example of a family of events (or hypothesis, concepts, etc.) such that the Sauer-Shelah lemma is tight.
The lemma states:
Assume that the Vapnik-Chervonenkis ...
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What inner monologue appears when you read Mathematical expressions?
When people are thinking, most of them have inner monologues. However, I'm facing problems because I don't know how to properly process Math expressions in my inner monologue. For example,
$$\mathrm{...
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What are good resources for a hard-working Calculus BC Student (offered only as a second year course in my highschool)?
I’m not sure if this is the best place to ask this…
I am currently a student in my school’s Calculus BC class, in which I would like to improve- not only in my actual grade, but actual abilities as an ...
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Proofs of basic, common, or concrete theorems in many branches of mathematics
I have several books of proofs such as:
$\color{blue}{\text{Book of Proof}}\text{ by }\color{green}{\text{Richard Hammack}}$
$\color{blue}{\text{Proofs: A Long-Form Mathematics Textbook}}\text{ by }\...
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What are the courses (other than mathematics) that are necessary to understand mathematics itself?
Physicists, computer scientists, engineers, (and many others) all study maths subjects beside their fields, because maths plays a critical role to understand such fields and to achieve required ...
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Taking hours on each exercise in Hartshorne chapter 1. What should I do?
I understand this could be off-topic, but I did not know other place to ask for help. Sorry, but please bear with me.
I am at graduating year of undergrad, and ambitiously approached an introductory ...
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Mathematical foundations of Reinforcement Learning
I'm trying to read and learn about Reinforcement Learning. I found that one of the most popular books about the topic is 'Reinforcement Learning: an Introduction' by Sutton and Barto. However in the ...
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How to Relearn High School Math In Greater Depth
I want to go back as far as necessary in order to relearn and solidify my understanding of foundational math concepts. I did not enjoy high school math and only completed the sequence up to Algebra II ...
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Is There Anything to be Learned from Very Long Computations?
While I understand that doing computations can help us gain a greater appreciation for the underlying concepts of our subject matter, it seems that sometimes textbook problems can become more an ...
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What is the benefit of asking students to regurgitate proofs of theorems on exams?
Almost two years ago when I was just starting to learn "university mathematics" I asked this question related to how much memorization should one do when learning math.
At that point I was (...
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What textbooks would you recommend to learn proof writing? [closed]
I am a high school student and want to pursue an undergraduate degree in mathematics in the near future. My teachers always emphasize the importance of mathematical maturity and the ability to write ...
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Is this book good for learning math for college physics?
The book Comprehensive Engineering Mathematics, by John Bird seems to be good also not only for engineering but also for university physics. Since as far as I can see it is applied mathematics. And it ...
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Learning Maths for Computer Science (Middle School level) [closed]
What is the most efficient method by which I can learn mathematics for computer science (beginning at a high school sophomore level)? Which subjects should I focus on, and which subjects should I omit?...
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Approximating an Ellipse given 4 points.
I am facing a problem in which I need to create masks for a certain region. This region is not a perfect ellipse, but for all intents and purpose, the ellipse needs to encapsulate these 4 coordinates.
...
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Question about demonstration of the type $A\Leftrightarrow B$
I have an important question when it is asked to us to proove affirmation/theorem wich look likes this $A\Leftrightarrow B$
I know that in order to proove $A\Leftrightarrow B$ i must proove first that:...
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Proof verification related to the Intermediate value theorem.
Suppose that f is a continuous function on [0, 2] such that f(0) = f(2). Show
that there is a real number ξ ∈ [1, 2] with f(ξ) = f(ξ − 1).
ξ ∈ [1, 2], ξ-1 ∈ [0, 1]
Case 1: if f(0)=f(1) then ξ = 2, f(ξ)...
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Is it possible to visualize, or make concrete, progressively more abstract mathematics? Are there mathematicians who can?
I'm really not good at math, and I'm trying to re-learn on Khan Academy. As I'm progressing, this question came up for me.
Learning math concepts that I can visualize in my mind or relate to some ...
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Consequences for mathematics of human writing conventions
When you learn to read and write, you learn that ideas flow on the page from left to right (or right to left, and occasionally from top to bottom, depending on culture). As you start to learn math, ...
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How does learning more about mathematics improve one's problem-solving skills?
The problem-solving skills in this question can be interpreted broadly as the skill or intuition to solve mathematical problems in general, or they can mean the skills in a particular field such as ...
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Can I read mathematics book without solving any problem in it?
I am reading "Topics in Algebra 2nd Edition" by I. N. Herstein.
In this book, there are too many problems for readers.
I want to understand this book but I don't want to solve problems if ...
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Introductory papers in Mirror Symmetry for algebraic geometry students
Assuming that a student knows algebraic geometry at the level of Cox's
(1) Ideals, Varieties and Algorithms
and
(2) Toric Varieties
What are some good papers (meaning, suitable in light of (1) and (2))...
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How to learn math after your PhD is finished [closed]
Question: How does someone go about learning advanced topics in Math after they're done with their PhD?
Specific example:
You've done your undergrad and masters degrees in math and learned from ...
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When "if P(x), then Q(x)" is false. How to explain it with truth table?
Question 1
$P(x) = x > 2$
$Q(x) = x^2 \le 4$
For all $x$ are real numbers, if $P(x)$, then $Q(x)$.
Put it simply. It is false for all $x > 2$.
But I am not sure how to explain each row in the ...
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How should one study Graduate Mathematics with a weaker background?
My question is: how should one go about studying graduate level mathematics when they have a weaker background?
This is probably a weird question since most of the people go in to graduate mathematics ...
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The proof of Fisher efficiency of the natural gradient method(Amari's theorem)
I am reading Theorem 2 of Natural Gradient Works Efficiently in Learning, Amari. It's about the fisher efficiency of the natural gradient method (NGD).
Let $D_T = \{ (x_1, y_1), . . . , (x_T, y_T) \}$ ...
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Students learning algebraic topology
In the preface of their book "Homotopical topology", Anatoly Fomenko and Dimitry Fuchs say:"Still, one can say that, from the students’ point of view, algebraic topology can now
be seen ...
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Looking for a discrete mathematics course by programming
Background: I am a totally blind programmer. That is, I cannot see at all. I am using a screen reading software to read texts, but not images. I am unable to get a computer science degree. Now I am a ...
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Will naming all theorems and results I go over in a textbook aid in learning? [closed]
Something I have always thought since working with math textbooks is that it is very opaque to refer to a result like "Theorem 8.2" or "Proposition 1.10". When I took my intro to ...
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Implications regarding limits
I'm currently working with limits in our Real Analysis course, and I'm currently struggling with certain implications regarding limits.
I can give you some examples:
If $f$ is bounded, then $f'$ is ...
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Recommendations and advices for self study and rigorous but in-depth high school math textbooks? [closed]
I apologize in advance for the long text, but I feel that I won't get a proper response without explaining my situation and my level of knowledge.
There are similar questions here but none of which ...
user964348
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Introductory, college-level math books based on _modern concepts_?
Has there ever been a more-or-less successful attempt to write a truly modern math book, say, on analysis or geometry, one rooted in the more abstract mathematics of the last century, that is ...
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Struggling with long computations. Any advice?
Sorry for the somewhat strange question but I have been struggling with this for some time now.
I am currently in undergraduate Electrical Engineering taking classes on Linear Algebra, Calculus and ...
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Recursive Least squares (RLS) for mini batch
I know that RLS can be used to update parameters being learned as they arrive.
This can be done efficiently for single data point and the derivations are easily available online and also easy to ...
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How a layperson in mathematics learn mathematics from basics to at least intermediate level?
From few weeks I have been watching videos on Mathematics and came across the mystery of prime numbers.
I am no mathematician, Even I almost know nothing about this field but I don't know I find Prime ...
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Why does $0.888888888889 \times 9 = 8$?
So I'm teaching myself maths, watching alot of youtube videos about topics way beyond my head. I'm trying to unlearn the rigid way school taught maths, such as the rules and procedures to solve ...
user938370
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stimulating budding math kids? (8 yo) [closed]
My 8 yo child loves maths, he considers it "his hobby". Without pressuring him, I'd like to offer him more challenge, wonder and marvel. The school can't really offer him more (tables of ...
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Is it recommendable to deepen the understanding of a subject just by doing lot of proofs?
In approx. 3 months I have an oral exam in complex analysis. I really have to do this exam well. By now I have a basic understanding of all topics which are relevant and now I am at the point to ...
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Intro to Proof Class: Understanding how to interpret $f \colon [0,1] \to \mathbb{R}$; $I: A \to \mathbb R$; $I(f) = \int_0^1 f(x) dx$
I am currently in a intro to proof class, so far I have had a good understanding of proof techniques but after moving onto functions I have become really confused on how to interpret some basic ideas:
...
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Is it worthwhile to redo problems where an arithmetic mistake has been made? [closed]
When learning new concepts in math, is it worth my time to redo problems if my mistakes were purely arithmetic mistakes (or very simple algebra mistakes)? If I made sign errors, or added fractions ...
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What are the most general and powerful math tricks?
I quote from the first chapter of Michael Spivak's Differential Geometry Volume I:
The precise definition of $\mathbb{P}^2$ uses the same trick that mathematicians always use when they want two things ...
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Learning Mathematics: unique knowledge of math.
I've come to a point where I now more fully (like 99%) understand that math is about specialized/unique knowledge which can't be summarized by some grand scheme or united principle.
So my question is, ...
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