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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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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1 vote
1 answer
71 views

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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0 votes
2 answers
40 views

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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3 votes
1 answer
102 views

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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2 votes
2 answers
50 views

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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6 votes
1 answer
116 views

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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-1 votes
1 answer
96 views

Soft-Question: Is it possible to visualize, or make concrete, progressively more abstract mathematics? Are there mathematicians who can?

This is my first post! 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 ...
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8 votes
1 answer
602 views

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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0 votes
2 answers
113 views

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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0 votes
0 answers
79 views

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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0 votes
0 answers
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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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3 votes
0 answers
133 views

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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1 vote
2 answers
141 views

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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3 votes
0 answers
137 views

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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1 vote
1 answer
68 views

Difficulty with exercises and results and commitment to memory

First of all let me say, I’m currently an undergrad, and whenever I say ‘exercises’, it shall mean those from the very basic chapters of every topic. So, whenever I go about solving the exercises from ...
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2 votes
0 answers
26 views

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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1 vote
0 answers
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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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1 vote
0 answers
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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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0 votes
1 answer
66 views

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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0 votes
0 answers
29 views

Weak learning classifier

I have a data set with $m$ points and an algorithm that satisfies the weak-learning condition (it always outputs a classifier with $60$% accuracy). Each classifier output by the weak-learning ...
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0 votes
1 answer
38 views

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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3 votes
0 answers
220 views

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 ...
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3 votes
1 answer
157 views

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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2 votes
2 answers
89 views

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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0 votes
0 answers
55 views

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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2 votes
2 answers
251 views

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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7 votes
2 answers
355 views

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 ...
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6 votes
4 answers
270 views

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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0 votes
0 answers
54 views

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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  • 351
0 votes
3 answers
90 views

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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  • 3
1 vote
2 answers
108 views

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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2 votes
1 answer
79 views

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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0 votes
0 answers
51 views

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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4 votes
0 answers
194 views

How hard do mathematicians have to work to learn? [closed]

So this is a soft question, but I'm looking for a collection of specific instances or stories that provide a reasonable breadth or representative picture. The target audience for this question is ...
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4 votes
0 answers
65 views

Trouble applying theory to practice

I am a first-year math student and I am having difficulties applying newly learned theory to problems. For example, my current calculus book is Real Analysis: Series, Functions of Several Variables, ...
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1 vote
1 answer
206 views

Relations between differential geometry and algebraic geometry

I am currently an undergrad student looking to study some algebraic geometry, I have heard that differential geometry is useful for intuition in algebraic geometry, but I have no background in that (...
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1 vote
0 answers
109 views

Can I do good math research if I am mediocre in graduate course?

I mostly got B's in my graduate courses like algebraic topology, differential geometry, algebraic geometry and etc, and I start to lose confidence and patience because of this. Is it still possible to ...
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  • 1,660
3 votes
1 answer
123 views

Studying theorems in mathematics

Most math classes are 1. Learn the big concepts/definitions 2. Present theorems/corollaries 3. Prove them. I presume it is essential to memorize the definitions and big ideas. However, real ...
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1 vote
1 answer
58 views

Iterative policy evaluation algorithm in "Reinforcement Learning" written by Sutton.

I am studying the reinforcement learning using the textbook entitled "Reinforcement Learning An Introduction," written by Richard S. Sutton. However, I got a weird point in the iterative ...
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7 votes
1 answer
134 views

How to "remember" the solution to previously solved problems?

Does anyone have tips on how to glean and remember, long-term, the key concepts from tricky brainteaser/Olympiad-style problems (or tough problems in general) that aren't just memorizing the specific ...
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4 votes
1 answer
209 views

Taking notes as a mathematics student

a couple of years back I was in class with a student that was copying notes in class from the whiteboard and after class he would make his own notes out of the already written notes (he would somehow ...
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33 votes
8 answers
1k views

Collecting math websites [duplicate]

I would like to know math websites that are useful for students, PhD students and researchers (useful in the sense most of the students or researchers—of a particular area—are using it). Maybe you can ...
5 votes
2 answers
325 views

How to study mathematics (Graduate level)

I know that normally, after attending class and understand the theorem and proofs, we will go directly to the problem and solve a couple of them, strengthening the concepts. Clearly, this is the best ...
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  • 1,660
-1 votes
2 answers
97 views

How To Learn Mathematics Basics [closed]

I wanna learn mathematics from zero to advanced which books should I read and which websites should I visit?
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-2 votes
1 answer
106 views

How to stay organised and productive as a mathematician? [closed]

Like first time I try to self study before the lecture then I make notes to have better understanding and comprehension. Then,I have notes during lecture , else I will feel sleepy and not able to ...
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-1 votes
1 answer
354 views

Is learning linear algebra fundamentally different from other mathematical fields and how do you actually learn it? [closed]

I am currently taking a linear algebra course and I have an issue I have never ever experienced before. I understand nothing. Nada. I have never been a genius, but I learn fast. I have never struggled ...
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  • 473
6 votes
3 answers
267 views

Introduction to p-adic numbers

I am a freshman and for a final project of a subject I have to give an introduction to p-adic numbers, I look for some sources (books, videos, articles) to be able to do my work, the only bases I ...
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1 vote
0 answers
57 views

What do you do in order not to forget what you have learned some time ago?

I have been trying to find ways to retain the Math knowledge I have previously learned, for example, last Spring I took Linear Algebra and passed it with an A, but now I can't remember the simplest ...
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1 vote
0 answers
67 views

Integrating the "flow" note-taking method in math classes

I've recently learned about the "flow notetaking method" found here and here, which is supposed to be a good way to learn while taking notes. It was actually created by Scott H. Young, who ...
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  • 69
7 votes
4 answers
303 views

Struggling to both understand and remember maths!

I hope it is OK to post this question here... I'm currently in my 2nd year of maths at uni (doing cal 2, discrete, prob/stat) and hadn't studied maths formally for about 15 years beforehand. In my ...
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