11
votes
5answers
583 views

Understanding mathematical texts

Please could you comment on following: I always wanted to know what mathematicians mean by "understanding a piece of mathematics". For example, I have just finished the second chapter from Rudin's ...
1
vote
0answers
71 views

How can I learn to think in probability given my background?

I have this question for some time now and I've decided to ask here. I'm a student of Physics and I'm taking a probability course. Currently I'm used to deal with Physics itself (mechanics, ...
1
vote
2answers
66 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 ...
3
votes
2answers
92 views

How many times should students repeat reviews? Frequency of repetitions? [closed]

The usual advice is that a math student has to read or study something "a couple of times" to appreciate it. But is there a narrow range of the optimal number? Any research on this? And what's the ...
1
vote
0answers
70 views

Exam Advice or Tips, specific for Undergraduate Math or Higher [closed]

What are some noteworthy, even rare suggestions for exams in undergraduate math or higher? I'm not interested in general advice that can apply to many different subjects, like ...
1
vote
1answer
78 views

How to remember modular arithmetic and divisibility results?

I tried reviewing the same material $\ge 5$ times, once every 2 weeks or whatnot. Withal, I query intuition like this. But I forget these results quickly or don't remember them 100% perfectly. But ...
2
votes
2answers
81 views

Does attempting numerous questions in Mathematics textbooks actually help?

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 ...
2
votes
1answer
93 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
vote
0answers
39 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
vote
1answer
65 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 $a + b + c = 6$ ...
10
votes
2answers
125 views

Dealing with Fatigue [on hold]

If all goes well, I am on the route to start a PhD in Mathematics next Fall. I worked very hard my undergrad years with little or no break and no travels. It is something I really regret. Now I have ...
5
votes
1answer
86 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 ...
6
votes
4answers
501 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 in an 'optimal' and innovative way. And my question is: What should the teacher know ...
7
votes
2answers
96 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, ...
3
votes
3answers
109 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 ...
6
votes
1answer
168 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
votes
1answer
107 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 ...
9
votes
2answers
755 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 ...
3
votes
1answer
392 views

Specific Advice/Tips to Streamline Studying Math [closed]

1, 2, 3, 4, 5, 6, 7, 8, 9: Notwithstanding these instructive threads withal, I'd like to ask about concrete aids/boons/ideas on learning and studying maths, with straightaway impact. They can be ...
2
votes
1answer
161 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 ...
0
votes
1answer
57 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 ...
4
votes
2answers
177 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 ...
4
votes
4answers
130 views

Resources to help an 8yo struggling with math

Friends of mine asked me for suggestion for one of their children (age 8) who had bad scores at the local Star test (the family is based in California). Both parents work, so they have also limited ...
4
votes
2answers
170 views

How to determine the big questions in a field of mathematics?

During my self-study (and soon to continue at a university) of mathematics, one thing I have been interested in is how to to effectively learn the material. An answer to a question provided by ...
4
votes
3answers
450 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
votes
1answer
99 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
votes
5answers
293 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 ...
258
votes
29answers
37k 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 ...
6
votes
0answers
116 views

How much of the content from past classes do people remember? [closed]

I'm currently a third year math student and I am preparing to take my GRE subject test. As I study for the test I feel as if I have forgotten much of the content from classes that I've taken in the ...
5
votes
3answers
199 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 ...
2
votes
2answers
266 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 ...
5
votes
2answers
327 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 ...
0
votes
1answer
285 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 ...
10
votes
2answers
2k views

Is it better to learn math before physics?

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
votes
2answers
498 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 ...
18
votes
1answer
323 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 ...
25
votes
3answers
563 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
vote
3answers
413 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 ...
6
votes
1answer
260 views

How to most efficiently remedy mathematical deficiencies

My spouse and I are currently both pursuing our undergraduate degrees. I'm double majoring in Computer Science & Mathematical Sciences and my spouse is double majoring in Economics & Finance. ...
6
votes
2answers
615 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 ...
2
votes
2answers
792 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
4answers
1k views

How do you rebuild your Math skills after college?

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 ...
10
votes
4answers
574 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" ...
5
votes
2answers
226 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 ...
2
votes
2answers
293 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 ...
6
votes
3answers
1k 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 ...
27
votes
8answers
3k views

Math every mathematician should know [closed]

Sorry in advance if this question doesn't belong here. I know it walks the line of what kinds of questions should be asked, but I'm really interested in what the community here has to say on it. ...
44
votes
9answers
3k views

Is memory unimportant in doing mathematics?

The title says it all. I often heard people say something like memory is unimportant in doing mathematics. However, when I tried to solve mathematical problems, I often used known theorems whose ...
151
votes
27answers
14k views

Too old to start math

I'm sorry if this question goes against the meta for posting questions - I attached all the "beware, this is a soft-question" tags I could. This is a question I've been asking myself now for some ...
15
votes
4answers
4k views

How to Improve Mathematical Thinking and General Problem Solving Skills?

I'm a sophomore in university and seriously feel that I'm bad at solving mathematical and algorithmic problems (be it discrete math, calculus or just puzzles). I noticed that I'm only good at solving ...