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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Recommend me math textbooks from prealgebra to undergrad level. [duplicate]

So I've been reading through math.stack exchange and physics forums and r/learn math to find a comprehensive list of math textbooks to learn math from the ground up. I'm more wanting to do so to ...
6
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4answers
720 views

Books for a beginner

I am a student of 11th grade and i have completed the syallabus of both 11th and 12th grade maths with complete understanding and it was possible coz of the love for this subject that i have. I don't ...
3
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1answer
114 views

About having everything well under control [closed]

When I started doing maths I "rediscovered" some elemental things and listed them on a notebook. All things I learned were in there, like Pythagorean theorem, sine and cosine definitions, some ...
4
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5answers
548 views

How important is a teacher / tutor?

I am doing fine in my classes and enjoy math. That is not the issue. During my spare time, I am doing more advanced stuff than my class is currently doing. My question is though, would I benefit more ...
292
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29answers
44k views

My sister absolutely refuses to learn math [closed]

My 13-year-old sister has a problem which, given the way math is currently taught, I doubt is anything but all too common. She has a low grade in her math course and only ever attempts to memorize ...
1
vote
2answers
366 views

Study regimen for discrete mathematics? - Lack high-school maths…

I have just gotten into college, and will be studying mathematics from next semester. (this course) Unfortunately I did not study mathematics for the last 2-3 years of high-school mathematics. What ...
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3answers
739 views

Why don't I understand “What is mathematics?” by Richard Courant [closed]

I am 14 years old and can do A level maths happily. However, I want to further my knowledge of mathematics to pave my way for more discrete maths and harder analysis etc. So I decided to pickup "What ...
0
votes
1answer
114 views

Problem with lowercase versus uppercase.

I often attack problems on two levels, a verbal level and a visual level. At a visual level, I try to imagine how everything is related - I arrange the ingredients of the problem into a two (or ...
1
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1answer
105 views

How can I prepare effectively for this test?

I live in Australia and I will be doing my final high school mathematics test in 5 months from today. The test is about the following topics: Differentiation and Integration and their applications (...
3
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1answer
222 views

getting started self study

I am 14 and currently in year 10 (uk). I am very interested in maths and intend to pursue it. I currently can do C1, C2, C3 and parts of C4 edexcel exam board a level mathematics. However, when i ...
5
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3answers
315 views

learning/teaching approach to rigorous math with the goal of improving

I will state this now: yes, this is a subjective question. But I feel the answers people give may benefit students. I want to get better at doing non trivial proofs. Real analysis is standard ...
7
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3answers
5k views

Is there a correct order to learning maths properly?

I am a high school student but I would like to self-learn higher level maths so is there a correct order to do that? I have learnt pre-calculus, calculus, algebra, series and sequences, combinatorics, ...
5
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4answers
1k views

The maths required for an economics degree

I have a degree in computer science and I wanted to do another degree in economics. However, my maths have been weak since high school always scoring slightly above passing rate. During my course of ...
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3answers
1k views

Working habits in mathematics [closed]

Short version of my question: What are good and motivating working habits for a mathematician? N.B. There are similar questions to mine: see this (how to read maths) or this (efficient study) or this ...
5
votes
2answers
535 views

In what order should mathematical fields be learned? [closed]

This could be considered a broader version of this question, with all fields. I know that when high-level maths are reached, the fields being to split quickly (i.e. specializing in this type of ...
3
votes
4answers
142 views

What math will I need in order to learn Microsoft's UProve?

I'm studying Microsoft's UProve (independent studies at 35 years old) and forget most of the Math I learned in college. I intend to proceed and learn the contents of this chapter of this book but can ...
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1answer
772 views

What branch of mathematics improves logical thinking? [closed]

So, that's the question. I dare to generalize it even wider: what branch of mathematics improves the general thinking ability, intilligence, the way the person thinks, and makes it more logical? I'm ...
8
votes
2answers
4k views

Is it better to learn math before physics? [closed]

It seems that a persons ability to understand physics at a high level is limited primarily by their understanding of math. It also seems to be more efficient to learn the underlying math for a ...
5
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2answers
1k views

How can I make sure I never forget.

I am currently refreshing my Elementary Algebra using Schaum's Outlines. I find them useful as they are choc full of exercises (Which I now realize is the only way to master algebra). I am worried ...
6
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2answers
458 views

Rigour vs intuition

Researcher David Tall has written in chapter one of Advanced Mathematical Thinking that ...
2
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2answers
121 views

Infinite series help

Are there any hard and fast rules for finding the sum of an infinite series? What suggestions would you have for someone new to learning them? Memorize identities? Also, what are the best resources ...
20
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1answer
392 views

Learning Aid for Basic Theorems of Topological Vector Spaces in Functional Analysis

I am self-teaching myself the basics of functional analysis (e.g. topological vector spaces), and frankly I am starting to get a migraine sorting out/organizing in my head all of the details/...
28
votes
3answers
915 views

Do free online collaborative solution manuals exist?

I'm not a mathematician by training and a rarely come in contact with mathematicians. For this reason I find solution manuals to be incredibly useful - reading them allows me to see how experienced ...
1
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1answer
65 views

From (almost) zero to knowledgeable in statistics

I work in (server) operations and it is not very uncommon for me to parse logs and try to make sense of some kind of metric. For some odd reason I have grown quite fond of it. Assume that I have ...
7
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1answer
1k views

Philosophy of learning mathematics (combinatorics)

How does one learn mathematics in depth and well? I think I may be studying mathematics incorrectly, or I could be doing it a lot more efficiently/effectively. Sometimes I feel like I need every ...
1
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3answers
830 views

Where to pick up learning math again?

In high school, I absolutely loved math classes. I took Calc in 11th grade, and then since have done just about nothing with math. Is there somewhere I go to see what math knowledge I still have/...
78
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6answers
17k views

Studying for the Putnam Exam

This is a question about studying for the Putnam examination (and, secondarily, other high-difficulty proof-based math competitions like the IMO). It is not about the history of the competition, the ...
2
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2answers
177 views

Recommended topics for Chemical Engineering grad. [closed]

I'm a Chem. Eng. grad. I did well in my math courses and I really like math. I've started digging for some more to learn on my own. I like applying math but I'm most satisfied when I have a deep ...
227
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7answers
16k views

Best Sets of Lecture Notes and Articles [closed]

Let me start by apologizing if there is another thread on math.se that subsumes this. I was updating my answer to the question here during which I made the claim that "I spend a lot of time sifting ...
6
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2answers
1k views

start mathematics from scratch

I'm sorry if this question goes against the site. I have completed my engineering in computer science; we were taught to get degrees only in our university :(. I love mathematics but time passed ...
5
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1answer
302 views

What should I be doing in a grad level math course?

I have an undergrad degree in an engineering field and switched to applied math for a PhD. In engineering, I have had my share of good and bad professors but I knew what I had to be doing during a ...
12
votes
4answers
229 views

Transitioning to Elementary School teaching and need some advice on bolstering my math skills

I'm an English major trying to make the transition to Elementary School teaching. For as long as I can remember, I've been extremely math-anxious and I've only done the bare-minimum level of Math work ...
4
votes
2answers
3k views

Math resources for electrical engineering?

I am considering electrical engineering as my field of study. However, my math knowledge might not be as good as it should be. What math books/resources would you recommend me to read?
5
votes
1answer
220 views

Study advice: The meaning of 'doing mathematics' [closed]

I am a former computer engineering student that switched to mathematics this semester. The only math I have is basic calculus and linear algebra, both thought in a "engineering way". Now I really want ...
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5answers
3k views

How do you rebuild your Math skills after college? [closed]

I minored in Math in college (B.S. Software Engineering), and went through advanced Calc, Differential Equations, etc. But about 6 months after I graduated I had lost all my formulas. Now, about 5 ...
5
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2answers
259 views

Flexible distance learning Mathematics programme

I am looking for a flexible Mathematics degree programme from a reputable institution. By flexible here I mean: Able to take the programme at one's own pace The option to complete the programme at ...
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4answers
686 views

How can I explain topology to my grandmother?

I was recently look at a post on tex.stackexchange about explaining $\LaTeX$ to the OP's grandmother. I was wondering, could the same thing be done for topology? Except in this case the "grandmother" ...
2
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5answers
2k views

How to learn differentiation?

I am having a confusion in learning differentiation. Can you please point me to some video tutorials which explains differentiation basics clearly for beginners?
5
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2answers
288 views

How does one best balance learning from a “problem based book” with supplementary material?

We all know that when learning math, one has to do more than just simply read - one must try to solve problems and work actively with the material. Many books try to force the reader to participate ...
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5answers
3k views

Relearning Mathematics

First post, I'll try to make it clear and concise. I've been spending the past few weeks watching all sorts of space and science documentaries and it's ignited my eagerness to learn more about these ...
15
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4answers
1k views

How to get more creative in Calculus

I'm currently doing Calculus I (one variable and some max- min problems with two variables as well), and I can follow most proofs and understand most of all chapters in the book. It seems tough that ...
2
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2answers
427 views

Studying Schedule [closed]

Currently I am studying, on my own, multivariate calculus, math statistical analysis, and physics. My question is, when you personally study multiple math and physics subjects, do you study a little ...
2
votes
3answers
109 views

easy activity to train finding pattern ability? [closed]

I realize that my math learning go wrong way. Wikipedia says math is finding pattern, formulating conjectures, and proving it. but my math learning didn't focus on them. memorizing formula doesn't ...
8
votes
3answers
3k views

Advice on Understanding Vector Spaces and Subspaces

currently I am studying Vector spaces and sub spaces. I enjoyed working with matrices and using the Gaussian-Jordon elimination and I also had no problems with cofactor expansion and determinants in ...
9
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3answers
395 views

Links to Online Videos of Good-Quality Lectures by Mathematicians

I am not trying to do anything new here, but I would like to start an activity that has been going on at Math Overflow. Hopefully, people here at the Math StackExchange can also enjoy the good stuff. ...
7
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1answer
739 views

Empirical distribution vs. the true one: How fast $KL( \hat{P}_n || Q)$ converges to $KL( P || Q)$?

Let $X_1,X_2,\dots$ be i.i.d. samples drawn from a discrete space $\mathcal{X}$ according to probability distribution $P$, and denote the resulting empirical distribution based on n samples by $\hat{P}...
3
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1answer
207 views

Exercise #26 from “Abel's Theorem in Problems and Solutions” by Alekseev

Exercise: Prove, that for every element $a$ of the group: $(a^m)^{-1}=(a^{-1})^m$, where $m$ is natural. On the #23 was proven that $$(a_1 \centerdot \ldots \centerdot a_n)^{-1} = a_n^{-1} \...
6
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2answers
301 views

How to 'analyze' problems in analysis; Computing $\int_0^{2\pi}\frac{1}{(a+b\cos(\theta))^2}d\theta$

If $a, b \in \mathbb{R}$ with $a > b > 0$, compute this ungodly thing; $$\int_0^{2\pi}\frac{1}{(a+b\cos(\theta))^2}d\theta$$ I'm really not a fan of complex analysis... I can't visualize what'...
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2answers
2k views

Intuition on the Orbit-Stabilizer Theorem

The Orbit-Stabilizer says that, given a group $G$ which acts on a set $X$, then there exists a bijection between the orbit of an element $x\in X$ and the set of left cosets of the stabilizer group of $...
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8answers
4k views

Math every mathematician should know [closed]

This question is meant as a companion to previously asked questions like Proofs every mathematician should know. More and more I'm beginning to see that there is just too much math to learn. ...