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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2answers
92 views

I still forget concepts even after answering numerous math problems

Note: this is particularly aimed at high-school/entry level college problems When I'm learning a new topic: 1) I read the theory given in the textbook at the start of each topic 2) proceed to read ...
1
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2answers
81 views

Should the theory be studied thoroughly before solving exercises?

Most of the books claim in the preface that the important part of the book is in the exercises, which makes sense considering that solving problems improves in great depth the understanding of the ...
6
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0answers
86 views

Strategy for self-studying after M.S.

For someone who has finished their M.S. degree in pure mathematics, what is a good way to keep learning mathematics within your specialization? Would you suggest reading research articles from ...
0
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2answers
181 views

Measure Theory or Set Theory?

Having taken Real Analysis I before (the seven first chapters of baby Rudin) I have the option to take Measure Theory now. However I am torn between that and Set Theory. Which course would you go for ...
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1answer
52 views

One and Two Tailed Independent T Test Questions

The city council for a small town has been receiving complaints from local law enforcement that citizens have been extremely uncooperative when pulled over for minor traffic violations. To remedy ...
2
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2answers
105 views

Does attempting numerous questions in Mathematics textbooks actually help? [closed]

Specifically for high school/college maths where the textbook contains numerous exercises with similar trivial examples - would attempting all of the questions actually be more beneficial than (lets ...
6
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3answers
261 views

Is math independent of our sensory experience? [closed]

I've been asking myself this and other questions in the field of philosophy of mathematics. Could we, if we were isolated from any kind of sensory experience, be able to learn mathematics? Also, what ...
0
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1answer
19 views

What test could I use to test $\mu_1$ and $\mu_2$ instead of $\bar{x}$ and $\mu$?

A single sample $t$ test is only against a sample and a population correct? Can it test against a population and itself or two populations? ie $\mu_1$ vs. $\mu_2$....if not what tests would you use ...
2
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3answers
114 views

Intuition - Divisibility results - If c divides some integers, then c divides any linear combination of them. [closed]

Not querying about proofs here. I don't want to memorize, thence are there intuitions or illustrations for them? As a student, how else can I remember these results? Origin - Elementary Number ...
0
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1answer
49 views

Tool to reteach Algebra?

I was never a very good math student and over the years, I simply forgot a lot of math. But sometimes it annoys me to no end, because I work in a mathematically related field (applied statistics) and ...
4
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1answer
183 views

Learning to understand proofs faster?

There are many books, written by highly decorated academics, which feature proofs that I can hardly comprehend in an acceptable amount of time. Roughly each week, it happens that I find myself having ...
1
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0answers
48 views

Any quick mental mathematics techniques?

I recently came across a very easy way to find the squares of fairly large numbers ($1$-$100$, but could be extended indefinitely), by using a simple formula. It does require you to know the square ...
1
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1answer
73 views

How to get better at inequality problems?

I really like inequality problems, but I've found that I have severe difficulties with ones that should be simple. I can prove something simple like this For positive $a, b, c$ with $a + b + c = 6$ ...
3
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2answers
116 views

Time managment while self-studying rigorous mathematical textbooks

Lately I have been introducing myself to Calculus.But I have an issue with time. Namely I have found that on average I need about 2-3 hours per page of material.This of course includes finishing all ...
0
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1answer
68 views

Nature of Points and Lines in Euclidean Geometry

It may be true that very few middle school student can grasp the meaning of lines and points in Euclidean geometry prior to a direct instruction. For example, it's possible that such a conversation ...
5
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1answer
85 views

Breaking Out of Algorithmic Thinking

I have been taught my whole life to solve math with an algorithm or method. My teachers in school trained us to identify patterns in equations and then use a method to solve it. No one has ever ...
5
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1answer
129 views

Software for basic math notes at 5th to 10th grade level (10 to 15 years old)

So I've looked around, here and otherwise, but sadly can't seem to find quite what I'm looking for. I don't know if it even exists, I figured it was worth trying to ask, though. I've found plenty of ...
1
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1answer
48 views

Math Mindeset: Historical Learning vs Generality of Concepts

I started math four months ago with modules like measure theory and topology. It was unavoidable to notice how many concepts are more general than what I thought before. For example the ...
6
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5answers
1k views

Teaching irrational numbers?

I'm interested in teaching the irrational numbers to high-school students, and I need your ideas on how to do this in an 'optimal' and innovative way. And my question is: What should the teacher know ...
1
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0answers
58 views

Studies on how the wording employed on the explanation of mathematical concepts helps students to learn?

I remember that I had to learn division in my childhood, I could handle all the other mathematical concepts that were presented until then but division was a real pain to learn, somehow the idea of ...
3
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1answer
260 views

Math Shock in graduate program

People call it Culture shock but I call it Math Shock... let me explain my Problem... First I am graduate student in a good university in USA ( I get scholarship from my country). Before I lived in ...
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1answer
49 views

Learning way and Resource for Complete math Subject. [closed]

I want to learn [self learning] Mathematics from basic.What is the order [like 1) arithmetic,2) Geometry,Etc..] to learn the maths? and what is the best resource to that particular subject?
3
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2answers
102 views

Information on crucial results concealed as exercises or neglected in a textbook

First, where can students find lists, information, or resources on the crucial results, inequalities, theorems, etc... which a textbook might not explictly feature or even bring up at all? Second, ...
1
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0answers
18 views

Looking for intuition for picking strategy on how many pages to flip

This question is going to sound more CS'y because that is my background. It also might be a bit vague but that is because I am not sure what the right thought process is in how to formulate it. I ...
2
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2answers
282 views

Ring theory : Completely lost and overwhelmed

Over the past 3( 9 sessions) weeks my professor has covered entire Part 3 - Rings from Gallian's Abstract Algebra which includes Introduction to Rings Motivation and Definition Examples of ...
3
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3answers
141 views

Question on Rudin sequences?

In baby Rudin, Rudin shows that $$\lim_{n \to \infty}\sqrt[n]{p} = 1.$$ In the proof of limit he tries to prove that the limit is $1$. So he takes $x_n = \sqrt[n]{p} - 1$. I have never noticed this ...
2
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0answers
182 views

Dynamic Geometry Software for Straight-edge and Compass Constructions

Geogebra is a very good dynamic geometry software. It has so many default tools, e.g. parallel line, angle bisector, tangent to the circle, inscribed and circumscribed circles, etc. But I want the ...
3
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1answer
100 views

How does one learn math from square one? [closed]

Ok, I know this is vague, but assume I never really had a good working knowledge of math in any area. I want to pursue X related work, which calls for X, Z, E, A, L, C, Q, etc. math. I realize that ...
1
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1answer
80 views

Suggestions for complicated math concepts that a child can understand

My son really loves math (so do both his parents, for that matter), and does well at it in school. I will give him math puzzles or tricks now & again, as well as introducing him to Khan Academy ...
8
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2answers
252 views

Advice in Bachelor Degree

First of all, I´m very sorry for my bad english, especially writing. Ok, for differents problems i´m studing a Bachelor degree in Mathematics. These degree is online. Now, the problem with my school ...
3
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1answer
96 views

Is there a math news website or publication (for mathematicians)?

I'm an undergraduate math and physics major aiming to pursue a Ph.D. in either pure math or theoretical physics. I don't read traditional newspaper or news websites, since in my opinion they are ...
5
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2answers
1k views

How to study abstract algebra

I am taking Abstract Algebra course at the university. We are doing chapters 1-20 from Gallian's abstract algebra text book. I am just doing assigned homework everyweek ( About 5 questions from each ...
2
votes
3answers
52 views

Commutativity or Distributivity - Which One to Use to DEFINE Multiplication of Negative Numbers?

It's easy to calculate $3 \times (-4)$, using the meaning of multiplication: $3 \times (-4)=(-4)+(-4)+(-4)=-12$. But it's not the case about $(-4)\times 3$! To DEFINE $(-4)\times 3$ we can choose ...
6
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1answer
186 views

Is the computer changing the way we teach and learn math in schools?

Back in school, what I got taught during school was labeled 'math', but it was actually 'rote arithmetics.' This seems to also be the case of many other people. Some came to hate it and never came ...
3
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1answer
115 views

New ways to light the fire again

Recently I've been studying a lot of analytic geometry and this subject made my motivation drop. The thing is, the courses aren't stopping and I'm beginning to lose the passion I had before. I need ...
2
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1answer
171 views

Resources for exploring math without a teacher

The ability to understand the beauty of math requires rigorous study. However, most people do not have access to the kind of training pure math requires. Many of my friends easily get interested in ...
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2answers
1k views

Learning Abstract Algebra for a graduate degree

I would like to do a graduate degree in mathematics, and I have a full year before I will be able to do so (for personal reasons). I mainly have my weekends available to study. I am interested in ...
14
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2answers
738 views

How to do math and help people

I am currently an junior math and statistics student at the University of Florida. For my whole life I have really enjoyed math and really do find a calling in mathematics. Math classes are the only ...
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1answer
785 views

Best way to learn from THEOREM-PROOF format?

I've always loved the theorem-proof format in textbooks, e.g. Hardy and Wright's Introduction to the theory of numbers. However, the problem is that I can't remember anything I read in this format ...
6
votes
2answers
400 views

Which books to study category theory?

I am an amateur math researcher in the field of general topology. I've set the purpose to learn enough category theory for my research. After reading Steve Awodey, "Category Theory", 2010, is it ...
0
votes
1answer
351 views

What is the order of math topics that people learn math in?

You know how they say to learn algebra first, then learn geometry, then trig, then calculus...etc? So after that, is there an order of what to learn next? If so, I'd like to know what comes after ...
2
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1answer
203 views

Math writing solutions

I will begin to learn in the university next month and I would like to know what is the best way to write math except from handwriting? I am not sure if to use a mathematical software, digital pen or ...
5
votes
6answers
185 views

When learning maths, should I review past topics?

So I've been learning maths from online video lectures and books for some time now and, as is probably quite natural, I have forgotten some of the stuff I've already read through. That'd be mostly ...
0
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1answer
65 views

relevant pure math for optimization

I'm interested in optimization generally. I don't know enough to break it down to sub-fields that I would work on. Probability and statistics seem relevant. What about calculus of ...
3
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0answers
134 views

Where to start?

I want to learn Mathematics but I don't know where to start. Sometimes I really get frustrated as I am a Software Engineering graduate (currently working) and I feel like I don't know anything about ...
8
votes
1answer
153 views

Is it a bad idea to study modern algebraic geometry without having any background in smooth manifolds?

I have a chance to take a course in algebraic geometry developed in the scheme theoretic setting and am considering my options. I have taken graduate courses in general and commutative algebra and ...
0
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3answers
228 views

Recommended math background for game theory

I recently got interested in some game theory applications to poker. I want to try some of them out programmatically, but a lot of the math is a bit confusing. I learn math on my own fairly quick and ...
2
votes
2answers
1k views

MOOCs for college-level discrete math?

Specifically I am looking for short lectures (and quizzes) on specific topics. (like Khan Academy offers) Topics I am learning about include; Intro logic-theory + set-theory Notation, negation, ...
6
votes
4answers
848 views

Self-learning Mathematics

My question is very elementary, but I hope that you will endure it. I am currently in a CS Master's program and I notice that my skills in mathematics are lacking. My calculus course was 10 years ...
4
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2answers
229 views

Training to actively learn, think and use mathematics studied and construct everything on ones own

Someone said this: "Memorizing the entire Swedish dictionary will never make you mastering Swedish. Same to Maths, the only way is to actively think & use basics you absorbed so far to practice ...