# 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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194 views

### 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 ...
1 vote
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 ...
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?...
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. ...
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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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)...
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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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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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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### 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))...
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 ...
1 vote
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 ...
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 ...
1 vote
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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### 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
84 views

### 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
82 views

### 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 ...
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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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 ...
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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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 ...
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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### 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 ...
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 ...
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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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 ...
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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### 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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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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1 vote
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 ...
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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### 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, ...
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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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, ...
1 vote
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 (...
1 vote
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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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
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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### 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 ...
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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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 ...
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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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?
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 ...
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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267 views

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
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
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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