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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2
votes
1answer
30 views

Vector spaces - Multiplying by zero vector yields zero vector.

Please rate and comment. I want to improve; constructive criticism is highly appreciated. Please take style into account as well. The following proof is solely based on vector space axioms. Axiom ...
1
vote
0answers
32 views

Vector spaces - Multiplying by $-1$ yields inverse element of vector addition.

Please rate and comment. I want to improve; constructive criticism is highly appreciated. Please take style into account as well. The following proof is based on vector space related axioms. Axiom ...
0
votes
1answer
48 views

Bridging the Gap Between Implicit Understanding and Formal Math

I use set theory on an implicit basis as a programmer; however, it's recently become necessary for me to expand into the formal world to explain my intent to decision makers that don't operate at a ...
2
votes
1answer
291 views

Looking for a math study/project-mate [on hold]

I'm a math major and was wondering what to do over this summer, since I'm not going for any internships/have any fixated family agenda. I was thinking of working out a book, like Spivak, or work on a ...
66
votes
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 ...
18
votes
1answer
890 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 ...
0
votes
0answers
32 views

How do you look for classic/normative/standard books about an established branch of mathematics?

If you want to immerse yourself in a branch of mathematics (e.g. linear algebra and linear optimisation) which is new to you, then you often look for standard books which you can rely on. You could ...
2
votes
0answers
43 views

How to model a real-world graphical structure into a mathematical formulation?

I am trying to learn how to model programming problems in a mathematical way. I am a software engineer, but have recently been running into road blocks where I can't solve some problems very ...
3
votes
0answers
56 views

Vector spaces - Multiplying by zero scalar yields zero vector

Please rate and comment. I want to improve; constructive criticism is highly appreciated. Please take style into account as well. The following proof is solely based on vector space related axioms. ...
4
votes
1answer
44 views

Vector spaces - If an addend adds nothing, then the addend is the zero vector.

Please rate and comment. I want to improve; constructive criticism is highly appreciated. Please take style into account as well. With one exception, the following proof is solely based on vector ...
0
votes
2answers
572 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 ...
3
votes
5answers
300 views

Proof of uniqueness of identity element of addition of vector space

Please rate and comment. I want to improve; constructive criticism is highly appreciated. Please take style into account as well. Proof of uniqueness of identity element of addition of vector space ...
1
vote
0answers
22 views

Another proof of uniqueness of identity element of addition of vector space

Please rate and comment. I want to improve; constructive criticism is highly appreciated. Please take style into account as well. The following proof is solely based on vector space axioms. Axiom ...
3
votes
0answers
58 views

Attemping Qualifying Exam Problems — and failing

My question is concerning learning strategy. I can solve the majority of the exercises in a typical graduate mathematics textbook like, say, Dummit/Foote's Abstract Algebra. To supplement my education ...
17
votes
5answers
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 ...
6
votes
2answers
518 views

Does anyone know of any good ways to get good at algebra without as much“grind” as doing hundreds of questions a night

I'm coming to a point in college where I can't avoid my math classes any longer. I need to get better at algebra so I don't flunk out of the class when I take it, however I've never been able to get ...
2
votes
3answers
35 views

Why $ (1- \sin \alpha + \cos \alpha)^2 = 2 (1 - \sin \alpha)(1+ \cos \alpha)$?

Why $ (1- \sin \alpha + \cos \alpha)^2 = 2 (1 - \sin \alpha)(1+ \cos \alpha)$? I am learning trigonometric identities one identity I have to proof is the next: $ (1- \sin \alpha + \cos \alpha)^2 = ...
6
votes
2answers
148 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
votes
11answers
13k 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 ...
13
votes
5answers
673 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
votes
2answers
63 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
votes
2answers
130 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 ...
155
votes
27answers
15k 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 ...
26
votes
3answers
598 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
votes
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
vote
0answers
53 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
62 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?
11
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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
votes
1answer
74 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
vote
0answers
26 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
votes
1answer
89 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
417 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
vote
0answers
74 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
votes
1answer
36 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
votes
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
votes
4answers
906 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
votes
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 ...
0
votes
1answer
33 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
vote
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
votes
2answers
419 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
416 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
votes
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
95 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
79 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
86 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 ...
42
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
votes
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
vote
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
votes
2answers
114 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 ...