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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0answers
59 views

How long should you study Mathematics each day if you want to get into a graduate school? [on hold]

I'm a university student (Junior now!) and I was wondering how many hours fellow undergraduates and graduate students study a day. I hear posts about how time doesn't really matter and that it's about ...
6
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2answers
107 views

The best balance in studying Mathematics?

I'm a student studying Mathematics at a university level. I've completed Single Variable Calculus, Differential Equations, Multivariable Caculus, Real/Complex Analysis, and Linear Algebra and I've ...
23
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11answers
12k views

How to start with mathematics?

I fell in love with mathematics a bit too late when I've already taken decisions regarding my future, career-wise. Now I would like to learn math on my own but I'm a bit confused as where to start. My ...
0
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0answers
27 views

How to merge coordinates to learn position in space [closed]

I'm implementing an algorithm in which many different points move around in 3-dimensional space, learning their best positions. Each number in the coordinate must be between 0 and 100. For example, ...
12
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5answers
650 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 ...
2
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2answers
62 views

Motivational example for complex numbers

Years ago I was introduced to complex numbers. In class we had been talking about the cubic polynomial and its solutions. At one point we saw an example where, when using the formula, one had to stop ...
11
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2answers
128 views

Dealing with Fatigue [closed]

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 ...
0
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2answers
557 views

Generalized eigenvalue solver online

For demonstrative purposes, I am trying to find an online solver where alumni can input data of two matrices A and B, then the system outputs the first eigenvalues and eigenvectors in the generalized ...
153
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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
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0answers
850 views

Efficient ways to read and learn a new topic

I started reading the book "Topology without tears" by Sidney A Morris and lecture notes on "Elementary Number Theory" by WWL.Chen. To get the maximum out of the book and understand the material ...
25
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3answers
576 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 ...
10
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13answers
2k views

False beliefs in mathematics (conceptual errors made despite, or because of, mathematical education)

Over on mathoverflow, there is a popular CW question titled: Examples of common false beliefs in mathematics. I thought it would be nice to have a parallel question on this site to serve as a ...
1
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0answers
45 views

Most Suitable Book after Kline's Calculus?

I've been working through Morris Kline's Calculus: An Intuitive and Physical Approach and it's an absolutely excellent book for self-studying applied single-variable (and some multi-variable) calculus ...
4
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0answers
58 views

Analysis or (abstract) algebra first?

Which one would you recommend? I only know calculus and linear algebra when it comes to university-level mathematics. Is one required to understand the other?
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6answers
9k views

Can I learn Calculus on the web, for free, using simple tutorials?

I'm a lazy type of person. I love experimenting with things before learning the theory. I like to practice, and learn from my mistakes. In 3-4 months I have a basic University exam on Calculus, and ...
0
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1answer
69 views

Book recommendations for someone interested in higher mathematics?

Background: I am currently studying physics and except for high school mathematics I have experience with linear algebra, single- and multivariable calculus, differential equations (mostly ODE's, but ...
1
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0answers
23 views

Are there online-platforms where to find people for joint learning and discussions?

After quite some time in academia I ended up in a nice company but the math to use is not really demanding. Hence I am still reading and working a bit on some university level math. It's roughly at a ...
2
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1answer
88 views

Does math have to be learned linearly?

I am asking because often times one doesn't know where to start in math. "Just learn what you need" is very vague and unspecific ... for example, assume I'm a beginner at Algebra and was considering ...
3
votes
1answer
414 views

Do only certain people exceed at math well? [closed]

It's obvious if you look around that math has always been one of the toughest subjects in all areas, from federal-traditional public schools to simply people learning it as an autodidact, hobby, or as ...
1
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0answers
73 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, ...
0
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1answer
35 views

The value of to fill the gap in the proof

I have studied a paper "On Finite Groups with Given Conjugate Types I" recently. The author use many words like "obviously", "clearly", "trivial", etc. in his proof. But these "obviously" implication ...
25
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3answers
3k views

Math Major: How to read textbooks in better style or method ? And how to select best books?

I'm a bachelor student of Math major. The question is about the better way to select and read maths text- or non-text- books, without considering the course and exam. (Because we follow the lecture ...
18
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4answers
873 views

Perspectives on Riemann Surfaces

So, I have come to a somewhat impasse concerning my class selection for next term, and I have exhausted all the 'biased' sources. So, I was wondering if anyone in this fantastic mathematical community ...
3
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4answers
134 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 ...
62
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9answers
4k views

Math and mental fatigue

Just a soft-question that has been bugging me for a long time: How does one deal with mental fatigue when studying math? I am interested in Mathematics, but when studying say Galois Theory and ...
0
votes
1answer
31 views

Intuition or wisdom for stability and instability properties of locally linear system. Boyce, p513, Table 9.3.1

Our instructor requires us to memorize this table for our differential equations exam. So I wonder if anyone has some deeper intuition or observation to help with this? For example, I noticed ...
1
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2answers
62 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
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 ...
9
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2answers
416 views

Automatizing computational skills

"It is a profoundly erroneous truism, repeated by copybooks and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise ...
3
votes
1answer
397 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 ...
8
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8answers
6k views

Where to go after calculus?

Ok this is a bit of an unanswerable question, but hopefully someone will answer. As I have been going through college & high school there has been a kind of "path" through which you learn math. ...
3
votes
2answers
94 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
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0answers
75 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
81 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 ...
43
votes
4answers
4k views

Do you prove all theorems whilst studying?

When you come across a new theorem, do you always try to prove it first before reading the proof within the text? I'm a CS undergrad with a bit of an interest in maths. I've not gone very far in my ...
11
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3answers
3k views

Why is it that when proving trig identities, one must work both sides independently?

Suppose that you have to prove the trig identity: $$\frac{\sin\theta - \sin^3\theta}{\cos^2\theta}=\sin\theta$$ I have always been told that I should manipulate the left and right sides of the ...
1
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1answer
49 views

Strategies for revising undergraduate mathematics

I'm a third year undergraduate maths student with exams (logic, set theory, Galois theory, graph theory) coming up. My present grasp on the material is, shall we say, lacking. My current system for ...
0
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2answers
108 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 ...
0
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1answer
30 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
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 ...
6
votes
3answers
211 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
votes
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 ...
4
votes
3answers
91 views

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

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 ...
2
votes
2answers
819 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?
0
votes
1answer
34 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 ...
2
votes
0answers
29 views

On ambiguity in statements expressed in natural language, where the statements use an indefinite article, e.g. “a”.

Please consider the following example statements and judge the meaning of the article "a". Example: A house is a building. Example: A house is being built next to our house. In example 1, "a" is ...
2
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1answer
98 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 ...
2
votes
2answers
740 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, ...
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votes
5answers
2k views

What's better strategy to handle tons of formulas, definitions?

I'm freshman, bachelor of Math major. When I read and learn the textbook, there're lots of formulas, laws, definitions and so forth. But what is the better way to handle it ? I mean, is it necessary ...
6
votes
4answers
525 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 ...