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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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How Can I Get Better On Combinatorics? [closed]

I am currently using this textbook to study applied combinatorics: Applied combinatorics, 6th edition by Alan Tucker. However, I have a super hard time doing anything that deals with the addition ...
Comet's user avatar
  • 9
11 votes
4 answers
2k views

How can I learn how to solve hard problems like this Example?

Preparing to the Math Olympiad , I found a book and decided to go through it as a summer project. I'm good at math but far from being an Olympian, yet I want to broaden my horizons - problems in this ...
Iruven's user avatar
  • 113
3 votes
0 answers
83 views

How to restudy functional analysis

I am re-studying functional analysis to prepare for my next year's PDE courses, I've taken it this year but I feel like I am not very good at it. May I ask what is the study routine/strategy for ...
HIH's user avatar
  • 477
0 votes
0 answers
50 views

Using A Proof Assistant as a Learning Aid

I don't see that anyone has asked this before, but if I have missed something please let me know. tl;dr - Can you use a proof assistant (like Lean) as a tool to learn math rigorously, and improve ...
RudyJD's user avatar
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0 answers
29 views

What is the optimal time one should spend on a textbook problem before deciding to seek the solution? [duplicate]

I’ve been grappling with a question that I’ve yet to find an answer to. I love solving math problems and I'm going to college this fall for a degree in computer science. Looking long-term, I would ...
ten_to_tenth's user avatar
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1 vote
0 answers
79 views

Prerequisites for neukirch algebraic number theory

What topics are prerequisites for studying neukirch‘s book algebraic number theory? I have studied Groups, Rings, Fields, Galois Theory, Linear algebra. But I have no idea what is commutative algebra, ...
Cosimo's user avatar
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3 votes
2 answers
534 views

How can I motivate and deal with speculation?

I am a student of mathematics and have been increasingly feeling doubtful about whether or not I really understand the theory. What I mean by this is highly attributed to the style of textbooks in ...
cpt.price's user avatar
1 vote
0 answers
43 views

Ways to learn mathematics [closed]

I will be graduating with my bachelor's degree in mechanical engineering, in a few months, but I want to pursue master's in mathematics after 2-3 years. To prepare, I am currently doing "Advanced ...
Rohan Garg's user avatar
0 votes
1 answer
85 views

Learning effective [closed]

today I got my midterm test result of Discrete math (It can only raise the grade). I got 63, which is above the average, but still I don't feel comfortable with that. I have 7 courses in the semester, ...
miiky123's user avatar
  • 215
-2 votes
1 answer
80 views

Is there anything currently that generates rejection from the mathematical community? [closed]

Is there anything currently that generates rejection from the mathematical community, as happened with the complex roots of algebraic equations?
FRED ANTHONY VIGORIA HUALLA's user avatar
2 votes
2 answers
111 views

How to train myself to not think visually for simple math problems?

I have a problem where it is often very difficult for me to solve simple math problems without thinking about them visually, but at the same time, I have poor spatial reasoning and so I'm unable to ...
asdfasdf's user avatar
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0 answers
82 views

Advice about a composite book or series on mathematics

My question is mainly about a good book or maybe a series of books which provide me a very a basic understanding of topic of mathematics on an University level. To be specific, is there any series for ...
Sarban Bhattacharya's user avatar
1 vote
1 answer
111 views

An inquiry about notation for divergence and curl

I am math enthusiast who is always trying to expand his knowledge. Now I have one inquiry about vector calculus: Is there any “better” or “more reputable” notation for divergence and curl? I have seen ...
user avatar
1 vote
1 answer
401 views

What is usually taught after Linear Algebra and Real analysis? [closed]

I am a self-learner who loves pure mathematics. I study mathematics alone without university and I don't have professor or advisor to help me (So I am not sure what I can learn next). I mostly study ...
pie's user avatar
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2 votes
1 answer
70 views

Help with GCSE/A-Level learning materials

I'm trying to help my nephew with his Maths for GCSE and A-Level (UK). It's been many years since I've done this. All the books I came across provide the formulae but don't explain how the authors ...
user170828's user avatar
0 votes
2 answers
105 views

Any short good introduction for mathematical proofs with minimal prerequisites? [closed]

My objective at this point is not to learn all and advanced mathematical proof concepts/techniques. At this point my objective is to get basic understanding of what is mathematical proof and learn ...
vasili111's user avatar
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1 vote
0 answers
792 views

Posterior distribution for gamma distributions

Im given the question: Given that the Gamma distribution likelihood $$p(y|β) = Gamma(y; α, β) = \frac{\beta^\alpha}{Γ(\alpha)} y^{α-1} e^{(-βy)}$$ where α is a positive constant and β > 0 is ...
mads grønbeck's user avatar
0 votes
2 answers
110 views

How do derivatives even work?

I'm a student currently looking into partial derivatives and was writing notes for a simple example. $$\require{cancel}\text{find the derivative with respect to x:}\\x^2+xy-y^2=8$$ I got to the point ...
Nathan Williams's user avatar
7 votes
3 answers
4k views

What are the essential skills and abilities for pure mathematics? [closed]

I am interested in learning pure mathematics and I want to be better at it so I want to know what skills and abilities are most important for this field so I can improve them. I have asked two related ...
pie's user avatar
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0 votes
0 answers
140 views

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 ...
Barbatulka's user avatar
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0 answers
19 views

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 ...
user10478's user avatar
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6 votes
1 answer
248 views

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 ...
wsz_fantasy's user avatar
  • 1,732
0 votes
1 answer
189 views

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 ...
Princess Mia's user avatar
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1 vote
2 answers
439 views

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 ...
Mikayla Eckel Cifrese's user avatar
-2 votes
1 answer
59 views

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 \...
jakeezie's user avatar
6 votes
1 answer
386 views

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 ...
Tiago Verissimo's user avatar
2 votes
1 answer
366 views

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 ...
y4nik's user avatar
  • 193
5 votes
6 answers
1k views

Why does it take me so long to solve relatively easy problems and what can I do about it? [closed]

I know that some people just take longer to wrap their head around some things, but I must say that this is quite annoying. I am currently a freshman math student and have encountered the following ...
l337n00b's user avatar
  • 573
27 votes
4 answers
2k views

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{...
AprilGrimoire's user avatar
2 votes
1 answer
169 views

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 ...
user1234's user avatar
1 vote
1 answer
133 views

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 }\...
Hussain-Alqatari's user avatar
1 vote
0 answers
57 views

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 ...
Hussain-Alqatari's user avatar
2 votes
1 answer
639 views

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 ...
Abastro's user avatar
  • 99
2 votes
2 answers
1k views

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 ...
Pepe's user avatar
  • 126
1 vote
0 answers
182 views

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 ...
Luca's user avatar
  • 219
7 votes
1 answer
691 views

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 ...
Luca's user avatar
  • 219
2 votes
0 answers
170 views

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 (...
user69503's user avatar
  • 487
3 votes
3 answers
956 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 ...
user avatar
1 vote
1 answer
152 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 ...
Stupidest Man in the World's user avatar
0 votes
2 answers
61 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?...
Eduardo Culloch's user avatar
3 votes
1 answer
1k 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. ...
Dfisher12's user avatar
1 vote
2 answers
59 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:...
X0-user-0X's user avatar
6 votes
1 answer
130 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)...
Matty33Anderson's user avatar
-1 votes
2 answers
241 views

Is it possible to visualize, or make concrete, progressively more abstract mathematics? Are there mathematicians who can? [duplicate]

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 ...
JBR's user avatar
  • 9
8 votes
1 answer
643 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, ...
Ethan Dlugie's user avatar
  • 2,368
0 votes
2 answers
476 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 ...
wsz_fantasy's user avatar
  • 1,732
0 votes
0 answers
114 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 ...
tchappy ha's user avatar
  • 8,750
1 vote
0 answers
214 views

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))...
Salazar_3854708's user avatar
3 votes
0 answers
246 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 ...
Salazar_3854708's user avatar
1 vote
2 answers
267 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 ...
Stats Cruncher's user avatar

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